







16 golfers 
20090318 

From Bill: We have 16 golfers. We golf for 5 days, in foursomes. It should work out that each player plays with each other player 1 time exactly.
I just can't figure it out.
Thank you in advance!
Bill Answered by Claude Tardif and Victoria West. 





A puzzling equation 
20181204 

From Manny: Hello,
Can you explain why this is wrong:
1 = (1)^3 = (1)^{6/2} = ((1)^6)^{1/2} = (1)^{1/2} = 1 ??
Thank you Answered by Penny Nom. 





Why 1/3 in the volume of a cone? 
20181020 

From Keith: In the formula for the volume of a pyramid, Volume = 1/3 * base * height, where does the 1/3 come from, intuitively? Answered by Penny Nom. 





Golf schedule for 12 players over 8 days 
20180903 

From William: We have a golf trip with 12 golfers
we are playing 8 rounds together......we want to mix the group up at best possible w/o too much overlap.......
thoughts? the math is way over my head...
even if we play the first 6 rounds with different partners, then the last 2 can be repeats ...or whatever the math works out Answered by Penny Nom. 





Graphing y = 2x  1 
20180312 

From Himanshu: Hi I Himanshu I having 1 doubt on 1 question this question of graph how to draw y=2x1 Answered by Penny Nom. 





A fraction of a mile 
20180106 

From Sierra: There are 5280 feet in a mile. what fraction of a mile is represented by 660 feet? Answered by Penny Nom. 





Four multiples of 10 
20170923 

From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? Answered by Penny Nom. 





Factorials 
20170727 

From dinesh: Is there any shortcut formula for multiply series numbers.
like
1x2x3x4x5.......x100 =? Answered by Penny Nom. 





3 consecutive multiples of 11 
20170722 

From nisha: using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363 Answered by Penny Nom. 





y = g(x + 1) 
20170627 

From Shamsudiin: HI there i am currently doing a level maths AS
I don't understand how to graph this Question y=g(x+1) i really need help please
please respond to this problem Answered by Penny Nom. 





Solve the equation completely cos 2x = 1 
20170608 

From Lava: Solve the equation completely cos 2x = 1 Answered by Penny Nom. 





A limit 
20170514 

From Soham: Find out the value of the following:
lim (x+x^2 +x^3 +.........x^n–n)/(x–1)
x→1 Answered by Penny Nom. 





A function which is onto but not onetoone 
20170416 

From Avinash: Define a function f(x):N>N which is onto but not oneone.Where N is set of natural numbers. Answered by Penny Nom. 





2^a, 2^b, 1^1 and 1^0 
20170317 

From Émile: If you had 2^a = 4 and 2^b = 4 you could assume that a = b right? Yet we can observe that 1^1 and 1^0 both equal 1, yet 1 = 0 isn't true. So if given a log base 1 number 1 the would the answer be 1 AND 0? Answered by Penny Nom. 





One millionth of one percent of 90,000,000,000 
20170116 

From Gene: What absolute number is one millionth of one percent of 90,000,000,000 Answered by Penny Nom. 





x^2 = 16 
20161212 

From A student: x to the second power = 16
what number solves the equation? Answered by Penny Nom. 





A 1.4 acre square 
20160628 

From Jamie: Dear Faithfullness,
I was previously to be purchasing a square 1 acre plot, which I believe was to have 209feet, 4 sides perimeter.
How big would a 1.4 acre site be?
In sq feet length ie original 209ft + (the adeed 0.4) Answered by Penny Nom. 





tan15° 
20160411 

From JOHN: find the exact value of tan15° in surd form. Answered by Penny Nom. 





The diagonal of a 10 acre square 
20160411 

From Derrick: I own 100 acre square of land. I want to run from farthest corner of property to farthest corner, Diagonally. How many miles would I have traveled? Answered by Penny Nom. 





tan inverse 1/4 
20160314 

From nazz: prove; tan inverse 1/4=1/3 cot inverse 52/47 Answered by Chris Fisher. 





Can you construct a regular 21gon? 
20160308 

From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference?
if there an online calculator i can us, or some other interesting trick?
tia
peter Answered by Robert Dawson. 





A 13 game bet 
20160228 

From farah: I'm trying to calculate the odds of a 13 game bet. Each game has 2 teams with 3 possible outcomes (win,draw,lose).
What are the odds. Answered by Penny Nom. 





Subtraction in a base larger than ten 
20160131 

From Jenalee: Hello,
So happy I found this site. I am having problems with bases. My question is 97B9  6A3A base 16 for both.
Please help. Answered by Penny Nom. 





A schedule for a league with 15 teams 
20151205 

From Zac: Hello,
I have a league schedule question. We have a league where we have say have 15 teams. Each team is to play each other twice during a 10 week session.
However each team tries only to play 3 matches(teams) per night(week).
How would we set up a random schedule for the 10 week session? Answered by Victoria West. 





A schedule for 12 high school golf teams 
20151115 

From Jason: I have 12 high school golf teams (A  L). There will be 4 games each week for 4 weeks. For each game, 3 teams play at a time (A vs B vs C). I would like it where no team plays the same team twice. Week four is my issue as I seem to always have a team or two playing the same team again. Is it possible to have each team play each other only once? Answered by Victoria West. 





The derivative of x^1/3 
20151108 

From omar: hi can help me
am teacher ask me about x^1/3 Derivation definition . Answered by Penny Nom. 





A 15 team tournament 
20151028 

From Joseph: We have a 15 team tournament. Each team plays all other teams. We need a schedule were each game has a work team. Thus at each fields we have two teams playing and one working. All teams need to play each other and also be a work team. Any help would be appreciated!! Answered by Victoria West. 





11 golfers over five rounds 
20151015 

From Leo: 11 golfers over five rounds. Will golf as 443. How to set it up so everyone plays at least once with each player. Answered by Victoria West. 





A schedule for 16 teams 
20151014 

From Ellen: I will have 16 teams. I would like to figure out how I can have 4 groups of 4 teams playing in hour increments, but never meeting more than once. How do I accomplish this? Thank you so much for any help you can give to me. . Answered by Victoria West. 





18 golfers playing four rounds 
20150909 

From Paul: I have 18 golfers playing four rounds. I want two 3 balls and
three 4 balls each day. I don't want anyone to play in a 3 ball
more than once and I don't want anyone to play with the same
person twice. I realise everybody can't play with everybody, I
just want the best you can do. Answered by Victoria West. 





Golf for 12 with a proviso 
20150707 

From Ken: I hope you can help me. I'm trying to put together a draw for 12 players in 3 groups over 4 days. One proviso, 2 players must play together in each round because they require the use of a golf cart. We are due to play in September this year.
Thanking you in advance for any assistance you can give. Answered by Victoria West. 





A fantasy football league 
20150611 

From Jason: Hello. We have a fantasy football league with 14 teams. The season is 13 weeks long and we would like to figure out a way to have two divisions of seven teams each with each team playing their interdivision opponents twice. Is there a way to set this up? I cannot seem to find a way to do it. Thanks! Answered by Victoria West. 





Golf for 14: 2 fourballs and 2 threeballs 
20150520 

From martin: I have to organize 14 players to play four rounds of golf. Each round comprise two fourballs and two three balls .
What's the best combination to ensure that each persons plays with as many of the others as possible without playing with somebody more than twice? Answered by Victoria West. 





n^2 is a multiple of 100 
20150330 

From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom. 





16 golfers for 18 weeks 
20150322 

From Rose: We could use a schedule to include the following:
16 golfers
4 foursomes
Each person plays once a week for 18 weeks.
No one plays in same foursome more than 1 or 2 times, or the least
amount of time.
Thank you for your kindness. Answered by Victoria West. 





What is 1000 billion billion? 
20150310 

From LeRoy: what does this mean? 1000 billion billion Answered by Penny Nom. 





Scheduling 12 for lunch 
20150105 

From Sabrina: I have 12 staff members that need to have lunch together 1 time each week. I am trying to pair them in a way that we each have the same amount of lunches in the same amount of weeks. Please Help! Thanks! Answered by Victoria West. 





1.5% of 1 trillion 
20141230 

From Kgosi: How much is 1.5% of 1 trillion? Answered by Penny Nom. 





How many square feet in 10 gallons of liquid at 1/4 in thick? 
20141114 

From Rich: How many square feet in 10 gallons of liquid at 1/4 in thick Answered by Penny Nom. 





A 10foot piece of PVC pipe 
20141021 

From David: A plumber has a 10foot piece of PVC pipe. How many 9/5foot pieces can be cut from the 10foot piece ? Answered by Penny Nom. 





211(base x)=152(base 8) 
20140909 

From Vaidehi: Find the base value (i.e. x):
211(base x)=152(base 8) Answered by Penny Nom. 





4 rounds of golf as three foursomes 
20140818 

From Christopher: For our golf trip, we will be playing 4 rounds of golf as three foursomes. We would like to have each person play with everyone at least once. Is this possible? Answered by Victoria West. 





1/3 of $320 
20140813 

From Student: Grade:5
Please help I got tutor for selective and this question is really
bugging me a lot what is 1/3 of $320?
plez answer quick before I fail :( Answered by Tyler Wood. 





Golf for 10 
20140812 

From Fred: We have 10 golfers playing 4 rounds: one 4some and two 3somes each round.
Can you suggest the best distribution of players? Answered by Victoria West. 





Golf for 15 
20140811 

From Brian: I am trying to arrange 5 rounds of golf for 15 golfers. We will play 5 in a group, 3 groups per round, 5 rounds. I would like everyone to play with everyone else. Secondary objective would be for no one to play with anyone else more than 2 times.
Thank you. Answered by Victoria West. 





16 golfers over 15 weeks 
20140711 

From Steve: I need a schedule for 16 golfers over 15 weeks, where each golfer is paired with a different golfer each week and plays 4 matches per week against 4 different pairs (each pair does not have to play each week) Answered by Penny Nom. 





A 14 team golf league 
20140711 

From Pat: We have a 14 team golf league that plays a 16 week schedule. Playing once per week, I need a schedule where each team plays every other team at least one time. Answered by Victoria West. 





A rotation schedule for 14 teams 
20140708 

From Daniel: I am organizing team activities for a summer camp. We have 14 teams and 7 rotations and 7 different games. every team will play a different game each rotation. Where I am having trouble is I would like each team to play a different team each rotation without a repeat. Is that possible? if so what is the formula? Answered by Victoria West. 





14 golfers, 7 men and 7 women 
20140706 

From John: I have to schedule 14 golfers, 7 men and 7 women, into 4 teams each day, playing for 3 days. So each player plays with as many different players as possible for 3 games. Answered by Victoria West. 





12 golfers 
20140623 

From Derek: I have a golf group that is set up as follows.12 players broken into 2 teams of 6.We play as a 4 ball ie 2 from each group.I am looking for a formular to have the 2 players from each group not play with each other again & also both of the 2 in each group not play with others in the other group more than once.I don't believe it is possible,so will accept as little duplication as possiblemany thanksDerek Answered by Victoria West. 





The ratio of 1:1:2 
20140620 

From FREDERICK: 3 girls shared some hair ribbons in the ratio of 1:1:2 what is the total number of hair ribbons if the third girl got 14 ribbons. Answered by prnny. 





10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball 
20140604 

From adrian: Hi,
We are off to Scotland on our yearly golfing trip soon.
Question is we have 10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball.
I would like to ensure that each golfer plays with the other guys an equal amount of times,
guess 3ish? and we share the amount of times each player plays in the 4ball.
Hope you can help? Answered by Victoria West. 





14 golfers for 13 weeks 
20140517 

From Judi: I want to schedule each of my 14 golfers to play each of the other girls one time during a 13 week period. We would golf in foursomes , threesomes or twosomes to make this happen. Can you send me a grid that would do this scheduling? I'm at a loss as to how to do it!! Answered by Victoria West. 





Golf for 14 players over 12 weeks 
20140516 

From Judi: How would I develop a playing schedule using foursomes and one twosome for 14 players who will play 12 weeks and each person would play all but one of the others? Answered by Victoria West. 





18 golfers for 5 rounds with a teaching Pro 
20140514 

From Maree: We are taking 18 golfers on Tour with a teaching Pro. There are 5 rounds of golf and we want everyone to play with the Pro once, but everyone else to play with as many different people as possible Answered by Victoria West. 





Eleven guys on a fishing trip 
20140513 

From Mark: Eleven guys are going on a fishing trip and want to rotate so everyone fishes with the other guys with the fewest number of repeats.
They want to fish in groups of two with one fishing alone for
three and a half days so will rotate seven times.
Is there a combination that works and what is it? Answered by Victoria West. 





A schedule for 2 teams of 10 
20140507 

From John: How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 110, Team B would consist of players 1120. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!! Answered by Victoria West. 





Golf :15 players over 4 days 
20140502 

From michael: We are playing with 15 players over 4 days. We plan to have 3 people in each group. A total of 5 groups with 3 players each. Can I arrange for each player to play with other players only 1 time? Answered by Victoria West. 





11 golfers going on a golf trip for 4 rounds 
20140501 

From David: I have 11 golfers going on a golf trip for 4 rounds of golf. I want to make sure that everyone gets a chance to play with everyone at least once but not more than twice.
Also, as we are n = 11, we will be composed of 344 everyday. I am trying to ensure that as few as people as possible play in the group of 3 (golf seems to be more enjoyable for whatever reason in foursomes). i have tried 3 differemt times and can seem to figure it out. Can you assist? Answered by Victoria West. 





2 teams of six playing each other 4 times 
20140501 

From Steve: I have 2 teams of six (Team A & B) playing each other 4 times.
Is it possible to have a player from Team A play with a different partner from Team A for each of the 4 rounds,
and likewise for Team B.
Whilst no player from either team plays an opponent more than twice during the 4 rounds? Answered by Victoria West. 





Golf League Schedule for 15 weeks and three flights 
20140421 

From bigdog: I need help setting up a 12 team (3 flights with 3 teams in each flight) 15 week league play schedule. Each team must play teams in there perspective flight twice during the 15 week season. Answered by Victoria West. 





A golf league consisting of 14 two man teams 
20140410 

From Kevin: Hello,
I need to make a schedule for a golf league consisting of 14 two man teams playing over the course of 20 weeks. I understand that each team will play at least once and I believe 7 teams will play each other twice over the course of the season. How would I generate this schedule. Thank you,
Kevin Perry Answered by Victoria West. 





12 golfers, 6 rounds 
20140327 

From Bill: I have a group of 12 golfers playing 6 rounds of golf. I am
looking for a pairings schedule that allows each golfer to play
at least one round in a foursome with each of the other eleven
players.
Can you provide me with a solution? Answered by Victoria West. 





12 golfers, 24 weeks 
20140327 

From George: I have 12 golfers and want to set up a season schedule that will avoid duplication of playing partners as much as possible. The saeson is 24 weeks long. Do you have a formula? Answered by Victoria West. 





13 golfers in groupings of 4, 3, 3 and 3 
20140326 

From Lennart: How can I organise 13 players playing in groupings of 4,3,3,3 for 3 rounds of golf in a way that all play with all others but a minimum of times with the same players(?)If possible, nobody should play in the 4 ball more than once. I would be grateful for an answer/proposal! Thank you, LR Answered by Victoria West. 





14 teams divided into two equal divisions 
20140318 

From C: We have 14 teams divided into two equal divisions. We want each team to play each team in their division one time and four teams from the other division one time. What is the schedule Answered by Victoria West. 





A schedule for 6 teams over 12 weeks 
20140309 

From Paul: So I have a question. I noticed you came up with ways to create schedules and we are having a really hard time making our lineup correctly. Basically we have 6 teams that will play over a 12 week period every Monday night. The time slots are 1 hr each playing at 6, 7 and 8. We would like each team to play 3 games at each time slot over the 12 weeks. Is this something that can actually be accomplished?
Thanks so much for your help! Answered by Eric Venables. 





Eleven golfers 
20140308 

From Leon: I have a group of 11 golfers wanting to play 10 rounds of golf in grouping of 4,4,3 .What is the best solution so that everyone plays each other as many times as possible Answered by Victoria West. 





A boxandwhisker plot with one whisker 
20140109 

From Susan:
Question from Susan, a teacher:
I read your answer to the question about could a box & whisker have NO whiskers.
It made sense to me. However I am preparing for my advanced class and I have a sample graph comparing box plots of data.
Several of the box have only 1 whisker. There is no explanation for this. Can you help me out. I cannot think of a data set that would produce this. Thanks! Answered by Penny Nom. 





Scheduling 10 people for 5 rounds 
20131120 

From Keith: Using golf as an example, I would like to schedule 10 people for 5 rounds with 2 groups of 4 and 1 twosome each round. I would like to minimze the number of times any one player plays with another. Can you provide an optimal schedule? Thank you for your help. Answered by Victoria West. 





A Holeinone on all four par 3's 
20130904 

From Robert: There are four (4) par 3's at a specific 18 hole course.
One member has the honor of making a Holeinone on all four par 3's.
It has taken him 8 years to do it!
How does one go about computing the odds of this TREMENDOUS accomplishment?
Respectfully,
Robert laffal Answered by Victoria West. 





14 golfers in two person teams 
20130904 

From Stewart: How to rotate 14 golfers in two person teams without duplication until all have been paired at least once. Play is once per week. Answered by Victoria West. 





The perimeter of a 1.4 acre square 
20130829 

From Destini: I cannot figure out what the perimeter for 1.4 acres of land
in the shape of a square. I have tried and tried and eventually
tried to use a calculator and I still can't figure it out. Can you
help me? Thanks!
Destini Answered by Penny Nom. 





A schedule for 18 golfers 
20130829 

From Brian: After searching the data base which helped me solve at least 3 other issues I have one more un answered question. I have 18 golfers split into 6 threesomes for 4 days of golf. What is my best option for a schedule mixing them all up as much as possible over the course of the 4 days Answered by Victoria West. 





More on the scheduling of 16 golfers in 4 rounds 
20130826 

From Peter: I see your formula for 16 players 4 rounds.
Is it possible to get the players into different groups each day.
E.G Player 1 in group 1 the first day,
Group 2 the second day,
Group 3 the third day,
Group 4 the fourth day.
Then so on through the players. Answered by Victoria West. 





Golf for 11 
20130814 

From Don: 2 foursomes and 1 threesome for 6 rounds of golf Answered by Victoria West and Harley Weston. 





A golf tournament for 12 people 
20130801 

From Brad: I've looked all over the web for a solution to this (including searching the archives here) to no avail.
We're doing a golf tournament with twelve people. Each person has a "handicap" that demonstrates their skill level. We have these numbers for each of the 12 players. We are trying to figure out how to schedule two rounds of golf with the most balance possible.
 We are playing two "real" rounds of golf (18 holes). There are four people per group.
 We want to split each round into two 9 hole games, which gives us a total of 4 games
 Halfway through (after 9 holes), you switch partners within the foursome that you're playing in.
 We want everyone to play with 4 unique different teammates
So say you start the first 18 hole round as a group of Players 1, 2, 3, and 4. Players 1 and 2 are a team, and players 3 and 4 are a team. After 9 holes, Player 1 would either be paired up with Player 3 or 4, and the other two players would pair up as well. Then the next day we will mix up the foursomes and do the same thing.
In terms of just pure scheduling this is simple. But I'm trying to figure out how to best balance the handicaps (simple average of each team's two handicaps works here). Assuming I'll need some sort of program or spreadsheet.
Any help or even a push in the right direction would be a tremendous help. Thanks in advance to anyone who wants to give this a shot. Answered by Victoria West. 





Golf for 16 
20130731 

From Graylin: I am going on a golf trip and we have 16 players and need to know a formula that will allow us to all play together at some point in the 4 rounds we are playing. If not possible please provide best case.
Thanks. Answered by Victoria West. 





16 golfers 
20130731 

From Pat: 16 golfers...3 nine hole rounds a day...for 4 days.
what are the best pairings for the fewest repeats of partners? Answered by Victoria West. 





10 guys playing 89 hole rounds 
20130719 

From Jason: I have 10 guys playing 8 9 hole matchplay rounds. I need to have everybody play the other 9 men, but need to limit them to only a 9 hole match between them. If we need to go 334 or 244 for a better solution, that may be possible. Answered by Victoria West. 





13 golfers playing 5 rounds 
20130703 

From Alan: i have 13 golfers playing 5 rounds. want everyone to play together at least once. Answered by Victoria West. 





13 golfers 
20130702 

From James: 13 golfers playing in 4 groups [4,3,3,3 per group] for four rounds.
Can it be scheduled so that no two people play together more than twice? Answered by Victoria West. 





16 golfers in 2 groups of 8 
20130615 

From Derek: we are 16 golfers.2 groups of 8."A" group & "B" group.We are playing 4 rounds,4 players at a time,2 from each group.We don't want to play with or against the same person twice.IE we want to play with 7 different people each day.Is it possible ?thanksDerek Answered by Victoria West. 





21 golfers 
20130527 

From Linda: A database search for a question on how to schedule 20 golfers in groups of 4 was very helpful ( Mona's answer referred to by C. Fisher 932008) I'm very glad I found this sight.
Our problem is we will have 21 golfers in the second half of the season. Is it possible to figure out that schedule? I assume we will have to include byes, but I'm not sure how to go about doing that.
Thank you. Answered by Victoria West. 





How can we draw the equation "x+y=1" in 3d? 
20130503 

From shimaa: how can we draw the equation "x+y=1" in 3d Answered by Robert Dawson. 





10 golfers playing four rounds 
20130409 

From Terry: I've searched "golf" and "golf 10" but don't see 10 golfers playing four rounds (each round having one foursome plus two threesomes, and no "flights" as in one earlier answer); each player playing at least once with a maximum number of the other nine over the four rounds? Answered by Victoria West. 





16 golfers over 15 days 
20130402 

From Mark: 16 golfers, each plays the other 15 golfers once each over 15 days.
played in four foursomes each day.
What is schedule that allows each golfer to play with other golfers an equal number of times? Answered by Victoria West. 





100 animals 
20130225 

From Jessica: You have exactly $100.00 to spend. You must get 100 animals.
The chicks cost $0.10 each.
The pigs cost $2.00 each.
The sheep cost $5.00 each.
You must get some of each animal.
How many of each animal can you get? Answered by Penny Nom. 





We have 10 golfers and four rounds of golf in two days 
20130205 

From Steve: We are having a golf tournament. We have 10 golfers and four rounds of golf in two days. We are going to break the group of 10 into two flights. Flight A and Flight B. We would like all members in Flight A to play one nine hole match against each other. All players in Flight B to play one nine hole match against each other. Could we play in groups of 4,3 and 3? What is the best way to make the pairings work? Answered by Robert Dawson. 





Golf for 17 
20130123 

From Richard: I have looked through the examples on your site but can't find one that suits. I am fiddling with one to see if I can get a result; but not confident.
I have 17 players playing 6 rounds in 3 groups of 4 and 1 group of 5. Two players will not be included in any 5 ball group. Can you help me please. Answered by Victoria West. 





Golf for 18 for 18 weeks 
20130122 

From Al: We have 18 two man golf teams and we play once a week for 18
weeks. We need a formula to schedule these teams so that they play
each other one time only. Answered by Victoria West. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Golf for 12 
20120910 

From John: To have 12 players in groups of 4 playing in 4 games with different people each day Answered by Victoria West. 





12 golfers, 4 rounds 
20120829 

From Paul: We have 12 golfers who will play four rounds of golf  how can we organize the foursomes so that each player has the most exposure to the other 11 players? Answered by Victoria West. 





A schedule for 6 teams and 37 games 
20120829 

From Giovanni: Hello, i try to prepare a schedules for 6 teams, and every teams will play 37 games before the playoff. How to make a schedules? thanks Answered by Victoria West. 





Golf for 16 in 7 rounds 
20120816 

From Elizabeth: Hello,
I am trying to sort out golfing for 16 guys for 7 rounds. However the twist is that the teams are broken down into 8 old boys vs. 8 young boys. Ideally, each of the players would only play each other once within their own team and then twice within all of the matches. Is that possible? Thanks for your help, my brain is hurting! Answered by Victoria West. 





The range of h(x) = 1/x 
20120811 

From Lucy: What is the range of the function: h(x)=1/x (and can you please explain why)? Answered by Penny Nom. 





A sand box with 14 sides 
20120710 

From Tom: Want to build a sand box for a pool that is fourteen foot round wanted to make it in fourteen pieces of wood what angle would each piece be and how long would each piece be Answered by Harley Weston. 





Expanded exponential form? 
20120612 

From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston. 





16 golfers, 4 rounds 
20120604 

From Gerry: 16 golfers, 4 rounds  best pairings so that everyone plays with each other at least once. Answered by Harley Weston. 





Golf 16 
20120529 

From marknp: 16 players only want tp play with one player each one time Answered by Victoria West. 





Division in base eleven 
20120527 

From Zoe: How do you divide numbers that are in base 11?
For example;
9A7A6A divided by A Answered by Penny Nom. 





16 golfers 
20120517 

From Nohemi: Can 16 golfers each play in foursomes for 6 days?
I found the answer for 5 days, but is it possible to do it for 6. Answered by Robert Dawson. 





Golf for 12 
20120420 

From glenn: need to schedule 12 players for a 20 week season Answered by Victoria West. 





Golf for 12 
20120420 

From Bram: We are heading on a golf trip with 12 guys, playing 6 rounds. Can you please provide the formula whcih which have the least duplication.
Thanks in advance,
Bram Answered by Victoria West. 





16 golfers 
20120420 

From steve: i have 16 golfers, 4 in "A" flight , 4 in "B" flight , 4 in "C" and 4 in "D"
We are playing 4 rounds (4 teams of 4) and every group must have a player from the A B C an D
flight, and in no round may 2 people have already played together! Answered by Victoria West. 





Golf for 12 
20120418 

From Brent: I have a golf group that is set up as follows: 12 players, broken into
2 teams of 6. I am looking for a formula to have one player from team A
play against one player for team B each round, not repeat the match, and
ride with as little duplication as possible. I know that it is not statistically
possible with these numbers and will have at least one round that has
duplication. Answered by Robert Dawson. 





Golf for 10 
20120418 

From Bob: Question from Bob:
Hi,
I am trying to set up pairings for 4 rounds of golf with only 10 golfers (2 foursomes and 1 twosome) and trying to minimize duplications. Any formulas or help? Answered by Victoria West and Harley Weston. 





A 14 man golf league 
20120412 

From Paul: 14 man golf league. Need to have alternating 2 man teams for 18 weeks. Need to rotate foursomes so no one is stuck in twosome more than once. Can you help? Answered by Robert Dawson and Victoria West. 





Golf for 17 
20120329 

From Richard: Hi Guys,
I have a scheduling problem which I don't think you have covered before.
Apologies if you have!
I have 17 golfers due to play 4 rounds of golf.
Each round will consist of 3 threeballs and 2 fourballs (ie. 17 golfers in 5 groups)!
Is it possible to come up with a schedule where each golfer plays
with different partners in each round? Answered by Robert Dawson. 





Converting from base 4 to base 10 
20111129 

From anjg: How to convert base 4 number 2^11 to base 10 number? Answered by Penny Nom. 





1 divided by 0 and infinity 
20111024 

From ritika: we say that one divided by zero gives us infinity, then why zero multiplied by infinity does not gives us one????????????? Answered by Robert Dawson. 





Expanded form 
20111012 

From Chris: Write this number in expanded form
4 326 180 501
Thanks!!! Answered by Penny Nom. 





Golf for 14 
20110711 

From Doug: We have 14 players playing over 4 days. can we play with different players every day and keep the 3 x foursomes and 1 x pair format Answered by Victoria West. 





Golf for 12 
20110707 

From Jim: I have a golf trip scheduled with a total of 12 guys. We are playing
three rounds of golf. For round 1 Players A B C D must play together.
Is there a formula that would allow me to set up the other 8 foursomes
with no repeats or minimal repeats?
Thanks. Answered by Victoria West. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





16 golfers and 8 rounds 
20110526 

From Gerry: 16 golfers and 8 rounds. To have each player play with as many others as possible. Answered by Victoria West. 





Arrangements of ten letters 
20110415 

From Mustafa: In how many ways can the ten letters of the word GELATINOUS be arranged
in a line so that the vowels are in alphabetical order (not necessarily together)
when read from left to right? Answered by Penny Nom. 





sin x = 0.25 
20110329 

From Wayne: How do you solve for x in the equation sin x = 0.25
the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom. 





The number of points on a line is equivalent to that of a surface 
20110324 

From Gary: I I was reading about how the number of points on a line is equivalent to that of a surface. This was done by taking any point on a line then taking alternating digits and making them as points on an x and y axis therefore points on a surface.The problem is as i see it if you just take a line then hold it over a surface you have just put the points on the line in a one to one correspondence with the points directly under it on the surface.Now you have all the rest of the surface which cannot be mapped onto the line since it is already used up.What am i missing? Answered by Penny Nom. 





1/0 and 2/0 
20110211 

From Dixit: How are the infinite number obtained by dividing 1 / 0 and 2 / 0 are different? Answered by Penny Nom. 





16 golfers 
20110122 

From Jack: I am responsible for setting up groups for 16 golfers for 7 days, is there a formula to calculate playing partners so that everyone gets to play with each person? Answered by Victoria West. 





16 golfers 
20110116 

From Kenneth: Our group will play 12 rounds.
We are 16 golfers.
How can I schedule 12 days of differing foursomes limiting repeats in the foursomes Answered by Victoria West. 





10 golfer playing 5 rounds 
20110109 

From Jeff: need pairing for 10 golfer playing 5 rounds of golf. Answered by Victoria West. 





Golf pairings 
20101217 

From AL: I have a golf tourney where we have fourteen players and are playing five times/rounds of golf. I am trying to pair up two threesomes and two foursomes so we don't play with the same person twice or the least amount of times. Answered by Victoria West. 





Draw a figure with 16 triangles using only 6 line segements 
20101216 

From Jill: How can you draw a figure with 16 triangles using only 6 line segements? Answered by Stephen La Rocque. 





Can a function be both even and one to one? 
20101009 

From Tracy: Can a function be both even and one to one? Answered by Harley Weston. 





12 coins 
20100707 

From Eden: We have 12 coins same in size and shape and also weight.
But among these, one coin which has same size and shape, but not in weight
and we can't know that this coin was lighter or heavier.
We must decide which coin was lighter or heavier among these 12 coins in
4 times of weighting with scale. Answered by Stephen La Rocque and Tyler Wood. 





More on carbon 14 dating 
20100526 

From Malachi: I am doing carbon 14 dating and i figured out the rule for taking the percent of the original C14 to figure out how old it is. how do I work the equation the other way around to find the percent remaining, from how long ago the objects organic mater died Answered by Harley Weston. 





The value of 1 acre 
20100513 

From Rebecca: If 38,121 sq feet equals $19,846.58 at 75% of its current value, what would the value of 1 acre be at 100% of value? Answered by Penny Nom. 





A 14 side well house cover 
20100312 

From Kenneth: I am 35 yr I am wanting to build a well house cover. I'm trying to figure out how long the pieces need to be and what angle they need to be for a 4 ft dia with 14 side well house. I would love an answer but would also like to know how to figure it in the future. Thanks Kd Answered by Harley Weston. 





The difference of the two numbers 
20100215 

From Steve: The difference of the two numbers 'abcdef ' and ' fdebca ' is divisible by 271. prove
that b = d and c = e. Answered by Claude Tardif. 





1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 
20100129 

From ireimaima: Hi..
Can u please help me with this question..
I find that when i test eg: n=2 for n (n+1) /4,
it seems that it does not giving me the right answer of 1^3 + 2^3 = 9
but 3/2... i'm confuse..can u please help me..thanks so much
Prove that:
1^3 + 2^3 + 3^3 +4^3………………………………..n^3 = n (n+1) /4 Answered by Penny Nom. 





15 golfers 3 rounds fivesomes 
20091223 

From Dewey: I have 15 golfers playing 3 rounds of golf. We will be playing in fivesomes. Any formula that has everyone playing with a different person each round?
Thank you.
Dewey Answered by Robert Dawson. 





Bases larger than ten 
20091214 

From Nick: For numbers in bases larger than ten, what are the digits by mathematicians' conventions?
I assume the first 10 are always 09. I know two computer science conventions (for hexadecimal (AF caseinsensitively) and for base 85 (casesensitivity plus 23 other characters)) and as a school student I learned that base 12 uses either T and E (which confused me when I thought they stood for Eleven and Twelve) or A and B, the latter as capitals only. Clearly, these conventions are in conflict.
I saw your reply in http://mathcentral.uregina.ca/QQ/database/QQ.09.99/magin1.html as accessed a few minutes ago but hope that in the 10 years since then mathematicians have arrived at a convention. Have they?
Thank you.

Nick Answered by Claude Tardif. 





Ascribing a value to 1/infinity 
20091119 

From Jack: Hello, and, in advance, thanks for answering.
I came across the problem of ascribing a value to 1/∞ (one divided by infinity) recently, I heard many things:
that it is infinitesimally small (i.e. .0000000000...1 the most intuitive), that it is 0 (the most ludicrous of them
all in my mind), and that it is not definable (which makes the most sense, although is a bit of a let down).
I know that lim (x>∞) 1/x = 0 and this is often used as an argument for all three possibilities. So
what's the ruling on this? And, I know this question has already been answered, but for a little modification;
is there any way to prove the answer that seems to be the most prevalently used (not definable as ∞ is a concept)
with mathematical logic? Or is it just because of the definition of ∞? Answered by Robert Dawson. 





Oneeighth of one million dollars 
20091116 

From Jarrett: what is 1/8 equal to out of a million dollars. Answered by Penny Nom. 





A 15 acre lot 
20090926 

From Ronald: The front and back are equal and the two sides are equal what would
what would be the dimensions of a 15 acre lot? Answered by Harley Weston. 





Dart teams 
20090918 

From Sally: I have 14 dart teams. Each team has a home bar.Usually it is one week home, the next week away. I have 3 locations that have one board only, yet have 2 teams at each location. I have one location that has 2 dart boards, and 3 teams. The last location have 3 dart boards and 4 teams.Can you make me a schedule that will be home and away, and every teams plays each other twice. In case you are wondering, the bars sponsor the teams.Thank you. Sally Answered by Robert Dawson. 





10 golfers 
20090906 

From Bill: We have 10 golfers scheduled to play over five days on vacation in November. Each day we will play in three groups of three and one foursome.
Is there an optimum solution that would assure that every golfer plays with every other golfer at least once while no golfer plays an inordinate number
of times with any other golfer or too often in a foursome? Answered by Victoria West. 





x^x = 1 
20090828 

From Waleed: x^x=1 Answered by Robert Dawson. 





Golf for 15 
20090818 

From Judy: We have a group of 15 golfers that play a scramble with groups of 3. The problem is we play for 14 weeks. We want every
player to play at least once with everyone and no more that 3 times. I am working on this and have just about accomplished
the schedule, but with a few playing more than 3 times. I'm sure there must be some mathematical calculation to do this but I
have yet to figure it out. Answered by Victoria West. 





A golf league with 12 players 
20090717 

From Jane: My weekly golf league has 12 players in 4 threesomes.
How many weeks would it take to play everyone once and not have too many
duplications? What would be the schedule each week?
Thanks Answered by Victoria West. 





Twelve golfers 
20090626 

From Fred: Hello
There are twelve golfers in 3 foursomes for three days. Is there a
combination of four man foursomes that allow for no duplicates? In
other words, is there a formula to insure the greatest amount of
variety in the foursomes. Looking at it math like you have
1,2,3,4,5,6,7,8,9,10,11,12 grouped into four numbers each for three
days. So if your have the first day 1,2,3,4 in one group, 5,6,7,8 in
the second and 9,10,11,12 in the third what can you do for the next
two days to have the fewest duplicates or have the greatest variety
in the foursomes?
Thanks Answered by Karen Meagher and Victoria West. 





11 golfers playing 4 rounds 
20090614 

From Brian: I have 11 golfers playing 4 rounds of golf. It would be great if we could play at least once with everybody. I realize we will have 2 foursomes and 1 threesome each round...can you help? Answered by Victoria West. 





Omega 1 
20090603 

From Justin: Hello there, I was just wondering if the infinity in the extended
real number system is the same as w1 (or Omega 1, the order
structure of the real numbers) in the transfinite ordinals? Thanks
so much for your help with this question, I really appreciate it!
Sincerely,
Justin Answered by Robert Dawson and Harley Weston. 





The sum of the angles of a triangle 
20090518 

From mary: prove that the sum of the three angles inside any triangle always add up to 180 degrees? Answered by Harley Weston. 





16 teams, 15 weeks, would like to pair up with no repeats. 
20090512 

From Kimberly: 16 teams, 15 weeks, would like to pair up with no repeats. Thank you so very much. Answered by Robert Dawson. 





A golf schedule for 18 teams 
20090421 

From laura: Could you help me form a golf schedule for 18 teams, playing a total of 8 weeks. Rotating the schedule each week so every team plays with a different team each week? I am using a shotgun format with 9 holes every week. Thank you for your input. Answered by Victoria West. 





The graph of y = 4x^4 
20090407 

From lyric: tell whether the graph opens up or down.write an equation of the axis of symmetry
y=4x^4 Answered by Penny Nom. 





More on the square root of 0.75 
20090330 

From Blaine: I read your response to How is the square root of 3/4 is greater than 3/4?
What I'm hoping for is a way for my students to use their own experience and number intuition to be able to make sense of the issue. As soon as my kids see "if y is this and x is this then..." their little eyes glaze over. Unfortunately, I can't come up with a way myself. Thank you for your help. Answered by Penny Nom and stephen La Rocque. 





0123456789 
20090325 

From Dr.: Many years ago I discovered that there are 33 numbers which,
when multiplied by 0123456789, simply rearrange the digits. Surprisingly
(to me at least) is the fact that the digits of all of those 33 numbers add up
to one of the 6 "cardinal" numbers 1, 2, 4, 5, 7, and 8. For example
6 + 2 = 8 and 62 X 0123456789 = 7654320918 etc.
Another interesting (to me) fact is that only the cardinal numbers
1, 2, 4, 5, 7, and 8 rearrange the digits in the number 9876543210.
My question is: "Is this known to anyone but me and the people I have
told?" Answered by Robert Dawson. 





A 14 team league that is divided into 2 divisions 
20090307 

From Ronnie: I have a 14 team league that is divided into 2 divisions. We have a total of 18 weeks to play. I would like for each team to play the team in their division twice. The remaining 6 weeks would be played with the other division. Any help would be appreciated. Answered by Chris Fisher and Victoria West. 





A shape with 10 sides 
20090303 

From Sandra: One of my son's math questions is as follows:
Suppose I have a shape with 10 sides. I choose a vertex then draw lines to the other vertices that dont share sides with the first vertex. How many vertices will that be and why? Answered by Penny Nom. 





16 golfers playing one round of golf on each of four days 
20090222 

From Jim: I have seen solutions for other combinations of setting up a golf trip but I haven't seen one for my group. We have 16 golfers playing one round of golf on each of four days. Is there a way for all of them to play in foursomes so that everyone gets to play with everyone else? Thanks for your consideration. Answered by Chris Fisher. 





Cantor's cardinality 
20090216 

From Justin: Hello, I was just wondering why the infinity from real numbers is smaller than Beth Two in the context of Cantor's cardinality set theory?
Justin Answered by Robert Dawson. 





0/0 and 1/0 
20090216 

From Justin: I was just wondering which is bigger 0/0 or 1/0?
Justin Answered by Robert Dawson and Harley Weston. 





12 golfers 
20090204 

From david: 12 golfers playing in 3 four balls over five rounds. can everyone play with
everyone else at least once. Answered by Victoria West. 





A 28 week golf schedule 
20090117 

From Don: You have a 12 man golf schedule playing 8 weeks. Can you
go further and make it a 28 week schedule. 3 foursomes. any help would be greatly appreciated. Answered by Victoria West. 





16 golfers 
20090111 

From Bill: I have read many of your answers to similar questions but still need your assistance.
We have 16 golfers that will be playing in 4 groups of 4 each day on an upcoming golf vacation.
Can you suggest the best way to scheudle the individuals assigned to each daily foursome
so that we have the most diversity in foursomes throughout the vacation. I am trying to have evryone
play with as many members of the group over the week with the least amount of repetition.
If you would please provide it for both 6 and 7 days, since we are not sure yet how many days
we will be playing.
16 golfersplaying in groups of 4 each day6 days
16 golfersplaying in groups of 4 each day7 days Answered by Victoria West. 





18 golfers and 5 rounds 
20090110 

From steve: We have 18 golfers 5 rounds .
Would like 3 foursomes and 2threesomes each day
Different groups each day. Answered by Victoria West. 





What is one trillion divided by 10? 
20081209 

From mark: can you please tell me what one trillion divided by 10 is Answered by Robert Dawson and Penny Nom. 





Aboriginal number groupings 
20080904 

From Barbara: Our current place value system is based on the notion of 10s. Did Aborginal people use a similar system or did they group numbers differently? Answered by Harley Weston. 





Divisibility by 11 
20080704 

From Peter: For what single digit value of n is the number n53nn672 divisible by 11? Answered by Leeanne Boehm. 





A golf tournament 
20080624 

From Roland: We have a golf tournament, 12 players, three rounds. We want to pair so that we have pairings with as few duplications as possible. Answered by Janice Cotcher. 





A 10 acre square 
20080512 

From RICHARD: I AM GETTING A 10 ACRE TRACT OF LAND OUT OF A 50 ACRE TRACT. ITS GOING TO BE PERFECTLY SQUARE.I NEED TO KNOW WHAT EACH PROPERTY LINE LENGTH WILL BE?ON ALL FOUR SIDES.AND THE TOTAL SQUARE FEET WILL BE IN THIS 10 ACRE TRACT? Answered by Penny Nom. 





Division by zero 
20080501 

From Bill: Why does multiplication have a favored status so as to make division by zero undefined? Answered by Harley Weston. 





WHY 144 where does this figure come from 
20080419 

From Sean: Why do you use the number 144 to divide
EG. length of timber 2 inches x 8 inches x 14 foot = 1.5 cubic feet
Calculation is 2x8x14 =224 divide by 144 = 1.5 WHY 144 where does this figure come from Answered by Leeanne Boehm. 





A 100 acre square pasture 
20080403 

From Richard: I need to know how many lineal feet there is around a 100 acre pasture that is square in shape. I am no longer able to get out and measure it myself, and cannot remember the math to compute it. Answered by Penny Nom. 





The product of two numbers is 1,000,000,000 
20080314 

From Henry: What two numbers that don't in zero when multiplied equals 1,000,000,000 and same with 1,000,000,000,000,000,000. Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20080207 

From ronni: why is the number 1 neither prime nor composite? Answered by Harley Weston. 





Multiplying decimal numbers 
20080205 

From alwyn: Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!!
In fact all Multiplying and or adding the value will go up and only when you subtract and divide it should become less !! Answered by Stephen La Rocque and Penny Nom. 





Multiplying numbers in bases other than 10 
20080108 

From Imaiya: In class we've been learning about numbers with a base other than ten. For example, base 7, base 5,
and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10.
I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base.
Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42
Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78
If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also
if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much,
and once again, thank you for your great site! Answered by Stephen La Rocque. 





Base 10 to base 5 
20071009 

From Angela: I've been searching online for the past week and I cannot find an Algorithm to convert from base 10 to base 5. Can anyone give me a stepbystep instruction on how to do this? Answered by Stephen La Rocque. 





Differentiate x^(1/3) using first principles 
20070914 

From Sheila: our teacher gave us this question as a challenge and even he couldnt figure it out:
Differentiate x^(1/3) [aka the cube root of x] using first principles. i know the answer is 1/(3.x^2/3), but how is it possible using first principles? Answered by Harley Weston. 





If A is 1 and Z is 26 
20070629 

From Sue: If A is 1 and Z is 26 is there a word that when you multiply all the numbers instead of letters adds up to a million? Answered by Chris Fisher and Harley Weston. 





An odd number with 12 factors 
20070627 

From Wilson: Do you know of any odd number that has 12 factors? Reply back today.
Because I have hand in a project tomorrow. Answered by Stephen La Rocque and Harley Weston. 





Where will volume 13 go? 
20070412 

From Shawn: A novice librarian shelved a twelvevolume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go? Answered by Stephen La Rocque and Penny Nom. 





Golf schedule 
20070330 

From Jim: I am organising a golf break for 12 golfers playing in 3 fourballs over 5 days. I would like to maximise the number of different golfers each player can play with. Any help would br greatly appreciated. Answered by Penny Nom. 





14 golfers6 days 
20070202 

From tom: 14 of us are going golfing over the course of 6 days is there a formula that would allow us to have the chance to play with as many different partners as possible2 foursome, and two threesomes Answered by Chris Fisher. 





A dinner group of 16 couples 
20061102 

From Nancy: This is a realworld problem. I should know the answer but I don't. A friend is starting a dinner group of 16 couples, to be distributed across 4 houses. Each month she wants to have a different set of host houses (no problem) AND she doesn't want repeats among pairs. That is, if the Smiths and Joneses are together one month, they should not be together another month until all the combinations have been exhausted. How many valid combinations are there? Is there a formula that I can convert into a computer program? I will have to get the names from my friend and give her back the combinations as she would not be able to deal with the math formulation. Answered by Denis Hanson. 





Golfing with 8 or 12 
20060213 

From Carolyn: I have a couple of questions that my dad asked me and I do not think it can be done in the manner he wants it to come out to.
He is going on a golf trip in June. There are going to be either 8 or 12 players playing 4 rounds of golf.
The questions that he says will not work and I do not know how to figure it out either is
4 Rounds of golf is for sure. 18 hole Rounds each
4 Players to a group
Either 8 or 12 players can every player play with every player in a group at least once during those 4 rounds.
If this can be done can you give me the combinations for both 8 and 12 , so I can help out my dad. Along with how you you figure this out. Answered by Penny Nom. 





A golf outing for 16 golfers 
20050805 

From Bob: I have a golf outing fast approaching and I’m having a problem matching the golfers so that everyone plays a round of golf with every other golfer in the group.
My problem is this: I have 16 golfers playing 5 rounds of golf. I would like a different foursome for every round of golf, that is each round (5 total) an individual is playing with 3 other players he hasn’t played with as of yet. Can you crunch the numbers and get back to me?
The way I see it, we have 20 combinations (5 rounds x 4 golfers) with numbers 1 thru 16. Answered by Chris Fisher. 





Divisibility by 15 
20041219 

From Lisa: My son was asked to find divisiblity rules for 15. We have been unable to find the answer. Does it exist? Answered by Leeanne Boehm and Denis Hanson. 





Divisibility by 7 and 11 
20041013 

From Tammy: I'm stuck in class in Yr 7 And I'm finding it hard on our new topic Divisibility! When I try to find out what this means on Internet sites i can not understand the used symbols like algebra and so on. I'm stuck on the divisibility rules for the number 11! Answered by Penny. 





Golfing with Norm 
20040819 

From Norm: I am organizing a golf tournament with 6 American and 6 Canadian players. We play 3 rounds of golf. Is there any way to arrange that everyone plays without playing with the same person twice. Each foursome must consist of 2 Americans and 2 Canadians with one of each in a cart. Your help would be much appreciated. Answered by Claude Tardif. 





The "22" puzzle and the "1089" puzzle 
20040422 

From Marcelle:
1. Choose 3 digits from 19
2. Make all the 2 digit numbers you can from these (6)
3. Add the 3 original digits and divide them into the sum from step 2.
The answer is always '22'. I just can't understand why. Can you please help.
Another one related to this is it:
1. Choose a three digit number ensuring the first and third digit are differnt by at least two.
2. Make the reverse three digit number and subtract the smaller one from the larger of these.
3. Take this answer and reverse it and add these two 3 digit numbers .
eg:
643  346 = 297
297 + 792 = 1089
it doesn't matter what numbers are used, the results are alwasy the same. eg 22 or 1089
Answered by Paul Betts. 





Equivalent sets 
20040306 

From A student: If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ? Answered by Penny Nom. 





A fifteen sided polygon 
20040305 

From Joann: WHAT IS THE NAME OF A FIFTEEN SIDED SHAPE? Answered by Penny Nom. 





Digits in the decimal expansion 
20040211 

From Leslie: In the decimal expansion of 1/17 what digit is in the 1997th place? Answered by Penny Nom. 





1/0 = ?? 
20031209 

From Lisa: One of my students asked me a fractions question. She knows that 0/1
equals 0 but does 1/0 also equal 0? Answered by Walter Whiteley and Penny Nom. 





A riddle 
20031119 

From Sarah: Ok, our teacher gave us this riddle, and I cannot for the life of me figure it out. He said that there are three problems with the following proof: Answered by Penny Nom. 





10,000 
20031008 

From Nathan: what two numbers make the product of 10,000. Neither number can end in a zero Answered by Penny Nom. 





Converting from base 10 to base 5 
20030910 

From Susy:
My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5. His first question of: 24(10) he has calculated to be 4x5 + 4x1 = 44 (5) The next question however is the tricky one.Ý We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it. 25 (10) = _________________ 100 (5) Can you help us figure out how we reach the answer. Answered by Claude Tardif and Penny Nom. 





Converting to base 10 
20030828 

From Karen: My son is in 5th grade.Ý He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.Ý Can you explain it to me in the simplest terms? Answered by Penny Nom. 





A golf tournament 
20030823 

From Dale: I am running a golf tournament with twelve golfers. We will be playing four rounds of golf. I don't want to schedule the same two players together more than twice (if possible). How would I make a schedule that each player would play at least once with every other player? I would appreciate any help that you can give me. Answered by Denis Hanson. 





39 consecutive natural numbers 
20030819 

From A student: Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Answered by Penny Nom. 





A function that is onto but not onetoone where f:N>N 
20021206 

From Lisa: A function that is onto but not onetoone where f:N>N Answered by Penny Nom. 





8 squares from 12 sticks 
20021008 

From A student: If you have 12 sticks the same size, how do you make them into 8 squares? Answered by Claude Tardif. 





11........1 
20020529 

From Un eleve: Démontrer que tout nombre impair non multiple de 5 admet un multiple de la forme:11........1 Answered by Claude Tardif. 





100 from four 9's 
20020327 

From A student: My teacher gave us a math problem to try and figure out and I am stumped. The problem was this.... by only using four nines, how can you get an answer of 100? You can add, subtract, multiply or divide...anything you need to do ,but you can only use four nines. Answered by Leeanne Boehm. 





When will the calendar be the same as 2002? 
20020220 

From John: When will the calendar be the same as 2002? I know the answer is 2013, but I don't know how to answer this mathematically, or if it is possible to do so. This is a ninth grade level algebra question my daughter received from her teacher. Any ideas? Answered by Chris Fisher, Patrick Maidorn and Penny Nom. 





What is 20 to the thousandth power? 
20020212 

From Kristi: What is 20 to the thousandth power? Answered by Paul Betts. 





Column doesn't add up to 100% 
20011017 

From A student: why don't some tables I'm studying in a column add up to 100%? Example: N=338, but responses to questions asked in survey I'm studying equal of 24.3, 9.8, 43.8, DON'T add up to 100%. I'm assuming that some people surveyed out of the 338 didn't bother responding, but is there another problem related to proportion or ratio being used, but improperly labeled on graph?. Note at bottom of table says: "number in parenthesis are numbers of cases" and 338 was in parentheses. I'm lost. Answered by Penny Nom. 





Dividing a circle 
20011017 

From Ahmeen: I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Answered by Walter Whiteley. 





The 100 chart 
20010928 

From Nich: Am I suppose to use the 100 chart for these questions. Question One: I am a 2 digit number my tens digit is 2 more than my one digit my 1 digit is between 4 & 6. What # am I ? Question Two: I am a 2 digit # I am greater than 40 but less than 60 my tens and ones digits are the same I am a odd number what am I ? Answered by Penny Nom. 





1:5 
20010927 

From Sandy: A colleague and I have a disagreement about dilutions. I seem to remember that I was taught (although it was a long time ago) that a RATIO was written thusly: 1:5 , and read " one part to five parts", for a total of 6 parts. On the other hand, a fraction is written: 1/5 and is read" one part in five" for a total of 5 parts. My colleague says that the ratio reads "one part in five" and is essentially the same as a fraction. Which is right? Have I been doing dilutions wrong all this time? I teach Animal Nursing and need to know where I can find a consise answer to such questions for making up medicated fluids, etc. Answered by Penny Nom. 





A 91gon 
20010910 

From Ashley: Hi! My name is Ashley and I am an 8th grader and I couldn't find the name of a polygon with 91 sides. i was a question from my math teacher. Answered by Penny Nom. 





1996^1999 and 1999^1996 
20010729 

From Rajesh: what is greater 1999^{1997} or 1997^{1999}? Answered by Chris Fisher. 





Where is the other $1? 
20010605 

From Samantha: 3 people go to a motel. The room is $30. They split it $10 each. While in the room the Mgr. tells the clerk the room was only $25, so he gives her $5 to take back to the 3 people. On the way she cant decide how to split the $5 between the three people so she puts $2 in her pocket and gives them $1 each.....Therefore, the room now only cost the three people $9 each, which is $27 plus the $2 the clerk pocketed,making a total of $29.....Where is the other $1? Answered by Leeanne Boehm. 





1 = 0.999... 
20010413 

From Joan: I have a middle grade math question for you. I would like to know why .9999... = 1 ? I can not use algebra to show this or the following: We agree that 2 = 2 and that 22 = 0, so
1.00000...... 0.99999.....  0.000000...... and 0.000... = 0 therefore 0.9 = 1 OR 1/3 = 0.333333 and 3 X 1/3 = 1, so if 3 X 0.333... = 0.999... then 0.999... = 1 My teacher says that I can not use the above example to show why this is true, and that I must use a couple different examples. He says that there are several other ways. Do you know any? I could really use the help because I can't think of any other ways to show this is true. Thanks for any help you can give. Answered by Penny Nom. 





4160 
20010307 

From Jessica: The product of two consecutive page numbers in this book is 4160. What are the page numbers? Answered by Penny Nom. 





Divisibility by 16 
20001212 

From Shiling: A number can be divided by 16 if and only if its 1st four digits can be divided by 16. How can you prove that? Answered by Penny Nom. 





Scheduling a golf vacation 
20001205 

From Michael: I'm having a problem scheduling matches for a golf vacation. We have 12 people playing 7 rounds of golf in 7 days. We play 2 man teams vs. 2 man teams everyday.Is there a formula so that you play WITH a different partner everyday and AGAINST as many different people as possible? Thank You for any help you may be. Answered by Penny Nom. 





Hendecagon 
20001009 

From Jillian: I need an example of a object that is in the shape of a hendecagon. I know what the shape is but I cannot come up with a real life example of an object that is this shape. Answered by Chris Fisher. 





1234567890 
20000914 

From Bradley Kloetzly: Can you find two whole numbers, with the smallest possible difference between them, which when multipled together equal: 1234567890? Answered by Harley Weston. 





Using the inverse sine function 
20000531 

From Nelson Rothermel: This has me completely baffled. I have to use the laws of sine or cosine to find the angles of a triangle when I have 3 sides, so I can't go 180xy when I have 2 angles. Now, I have a triangle with values of 3, 7, and 9. Here are the steps I used (A,B,C are angles; a,b,c are opposite sides): angle A (16.1951 degrees): cos^{1}*((b^{2}+c^{2}a^{2})/(2*b*c)) angle B (40.6011 degrees): sin^{1}*(b*sin(A)/a) angle C (56.7962 degrees): sin^{1}*(c*sin(A)/a) If you notice, A+B+C does not equal 180. According to the book, A and B are correct, but C is supposed to be 123.2038 degrees. Why doesn't it work??? Answered by Harley Weston. 





A 100gon 
20000524 

From Chris Mohr: What is a 100gon called? Answered by Harley Weston. 





The square root of 1 
20000519 

From Gary: i am not a student i am just some one that heard something and i can't be sure on the answer...my ? is what is the square root of 1? i think it is 1 but not sure can you let me know please thank you Answered by Harley Weston. 





2^32 + 1 
20000408 

From Un Etudiant: 2^{32} +1 can be divided by 641 , why? Answered by Claude Tradif. 





1000 percent 
20000317 

From Matt Stevenson: If one invests $4000.00 and makes 1000% on the investment would he/she have $40,000.00? Could one figure this by: $4000.00 * 10.0 = $40,000.00? So is 10 times a number the same as 1000%? Would 100 times a number be the same as 10,000%? Answered by Penny Nom. 





More on googols 
20000223 

From Kevin Brennan: Could you please give me a couple of examples of when you MATH guys would use a google. Do youu measure, like, galaxies with it ? Or was it created to keep track of Mr Gate's bank account. Answered by Penny Nom. 





Bases other than 10 
19991206 

From Garret Magin: We are doing a lesson on numbers of other bases than 10. We are working with binary, octal, and Hexadecimal. I was wondering what is used to represent number of different bases other then 16? Does it just continue on with the alphabet and if so what happens when you get to Z. It would be a help if you could answer this because it is really bugging me. And none of the math teachers at my school could let me know. Answered by Claude Tardif and Patrick Maidorn. 





Nines and ones 
19991105 

From Greg Miller: Using the numbers 1, 1, 9, 9, only once each, how can I create an expression that equals 10 using only the basic functions of addition, subtraction, multiplication, division, and/or parentheses? Answered by Claude Tardif. 





A googol 
19991006 

From Kevin Brennan: describe to me a guegoll is that how u spell it? it sounds like that Answered by Penny Nom. 





111...1222...2 
19990811 

From Brad Goorman: Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2. Express N as the product of four integers, each of them greater than 1. Answered by Penny Nom. 





Base 2 to Base 10, conversion, convert 
19990508 

From Larry Bader: 10100011_{2} is the same as what number in Base ten? a. 83 b. 128 c. 93 d. 326 e. 163 Answered by Penny Nom. 





Large Numbers 
19990405 

From CK: Hello. I need a lesson plan for grades 4 to 7 dealing with the concept of large numbers. Specifically, how to teach scientific notation. The lesson plan has to deal with the following: the size of the universe is so huge that is is almost beyond the ability of the mind to comprehend. One way is to measure... Answered by Chris Fisher. 





Root 17 is Irrational 
19990121 

From John Murdock: If you could help me out with this I would appreciate it. Prove that the square root of 17 is irrational. Answered by Harley Weston. 





Place Value 
19990105 

From Reg: I work in a Section 27 classroom with various grades. I am looking for assistance on how to deliver a lesson on place value:decimal numbers keeping in mind that they need to see it (visual) to comprehend. I am looking for grade 46 level. Answered by Jack LeSage. 





Golf Problem  The Sequel 
19981113 

From Bob: Sixteen golfers, seven rounds. What are optimum combinations for each golfer to play with as many different golfers as possible? Many thanks, Bob Payson Answered by Denis Hanson. 





Divisibility by 11 
19981028 

From Pat Duggleby: I am an upgrading instructor at a dropin program in Regina. One of my students is taking General Math 30 through correspondence, and we have run into some confusing instructions. The section is about divisibility rules, and we did just fine up until the rule for Divisibility by 11. The statement is as follows:  If the difference between the sum of the oddnumbered digits and the sum of the evennumbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11.  . . . Answered by Penny Nom. 





3 to the power of 1994 
19980905 

From Kim Tangney: What are the last two digits of:  3 to the power of 1994
 7 to the power of 1994
 3 to the power of 1994 + 7 to the power of 1994
 7 to the power of 1994  3 to the power of 1994
Answered by Penny Nom. 





Golf problem 
19980825 

From Bob: Twelve golfers plan to play seven rounds of golf. Each would like to play as many rounds with different golfers as possible. What are the optimum combinations to accomplish that goal? Answered by Denis Hanson. 





The sum of the angles of a triangle is 180 degrees 
19980219 

From Quin Liu: How do you prove that the sum of the angles of a triangle is 180 degrees? Is there a proof? what is it? Answered by Chris Fisher. 





un jardinier plantent 10 arbres 
20070930 

From yannick: un jardinier plantent 10 arbres.il a reussi a les disposer en formant 5 ligne de 4 arbres. retrouver une disposition possible Answered by Claude Tardif. 





1 exposant 4 
20041219 

From Denis: ma question est : 1 exposant 4 = ? Quand nous avons une base négative sans parenthèse comme ma question Answered by Diane Hanson. 

