







f(x + 2) 
20190226 

From a student: How do you use f(x) = 3x+1 to determine the transformed function of f(x + 2)? Answered by Penny Nom. 





A triangle made from 12 matchsticks 
20190120 

From Palesa: How many different types of triangles can be made with a perimeter of 12 matches? Answered by Penny Nom. 





Ten games with two possible outcomes for each game 
20181222 

From Jin: I'm trying to make a list to view all the possibility.
An example is if I have 2 games there's two outcomes (home/away)
I will use number to represent the teams.
01,23
All possible out comes are 02,03,12,13 right?
MY QUESTION If I have 10 games each have 2 outcomes (home/away) to win
What is all possible outcome.
01,23,45,67,89,1011,1213,1415,1617,1819
Could u please provide me with a list of all possible out comes
Thanks you 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. 





The sum and difference of two numbers 
20180830 

From Saranya: Hi,
The question is to find the numbers from sum and difference.
The Sum = 14 and the difference = 2
I found in this web site some useful answers. but my kid is going second grade only. She don't know how to do a division or multiplication.
So can you please explain on how to find the answer using only the Addition and Subtraction.
Thanks in advance. Answered by Penny Nom. 





Solve when the variable is in the exponent 
20180315 

From Dan: 50 x 2^n = 1,000,000
2^n = 20,000
what does n equal? 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. 





The intersection of a curve and a line 
20180308 

From lola: find the set of values of constant C for which the line y=x+c intersects the curve y=2 square root x at, at two distinct points Answered by Penny Nom. 





Average price 
20170915 

From Annette: If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price 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 25 acre strip 
20170529 

From Va: hello, can you pls help me....i have a property which has 300 ft width road frontage and my lot is 4700 ft deep to the back line of my property which i am told 27 acres. I want to only sell 25 acres...and go to the rear line with 4700 feet, but decrease the front width using the 300 ft measurement. how do i decrease the 300 ft width measurement by 2 acres? i am confused what the measurement would be..thank you....so to sum it i want to make 25 acres out of a measurement of 300 x 4700 ft long reducing the front measurement..thank you so much. Answered by Penny Nom. 





Rational numbers between 2 and 3 
20170408 

From Medha: Find 12 rational numbers between2 and 3 Answered by Penny Nom. 





Is the square root of 2 plus the square root of 2 irrational? 
20170329 

From haya: how can i prove the the square root of 2 plus the square root of 2 is an irrational number? Answered by Penny Nom. 





Is a large integer divisible by 2^n? 
20170328 

From Sahand: You are given number x that is very large (that large that it can't be divided by hand)
can we find out that x is divisible by 2^n or not? 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 2 million gallon tank 
20160928 

From Kimberly: I have a tank that is shaped like a cylinder, and it has to hold 2 million
gallons of water. There is a height limit of 30 ft.
I know the equation is V=pi x r squared x h but I don't know if I need anything
For the square foot of water. Answered by Penny Nom. 





Two pieces of rope 
20160521 

From Render: Fred cuts a 12 inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain. Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





20 mangoes 
20160401 

From Mussharat: I have 20 mangoes and have to put them in 5 boxes such that
the numbers will be odd numbers.Also I can't cut or take the seed
out from the mango . What should I do. It's really confusing.
I'll be more than happy if you could help me. Answered by Penny Nom. 





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 2 digit number 
20160208 

From Lloyd: The sum of digits of a certain 2 digit number is 7.
Reversing its digits increases the number by 9.
Find the number Answered by Penny Nom. 





Linear equations in two variables 
20151213 

From priya: I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9 Answered by Penny Nom. 





20 golfers playing a 20 week season 
20151207 

From Jeff: We have 20 golfers playing a 20 week season. We play in foursomes. How best to set foursomes so everyone can play with every without playing with the same person multiple times? 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. 





A six team league to play a 20 game schedule 
20151019 

From Kelly: Hi there. Some of your posts are close, but my problem is evening out the home
and away games. We have 6 teams in our league and we are going to play a 20
game schedule, playing everyone 4 times. We will play Fridays and Saturdays,
each weekend. Of course the ideal would be to have each team have a home and
an away game each weekend, but I realize that is impossible, but I would like it as
close as possible. Any help would be much appreciated!! We also were considering
opening with a home and away  Friday then Saturday with the same teams. Then
carrying on with playing everyone else and then possibly finishing up with the same
home and home Answered by Victoria West. 





32 golfers playing 6 rounds 
20150919 

From scott: i am looking for a schedule for 32 golfers to play 6 rounds and never play with the same person twice.
I made one for 28 golfers but i am struggling with 32. Answered by Victoria West. 





20 golfers for 6 days 
20150911 

From Dave: have 20 golfers for 6 days. Each player should pair with 18 golfers
used a system on your website which is good for 5 days, but cannot get the 6th day.
Thanks for your help Dave Answered by Victoria West. 





Factor x^2 + y^2 
20150826 

From Jerome: Factor: x^2+y^2 Answered by Penny Nom. 





A two digit number 
20150821 

From Cameron: Write the 2 digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is ________. Answered by Penny Nom. 





20 golfers playing four rounds 
20150817 

From Paul: I have a party of 20 golfers playing four rounds in fourballs.
I realise that everyone will have 7 players that they do not play
with, however I want to ensure that no one plays with the same
person twice and that the Captain plays with the 12 players of
his choice. 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. 





Is 22/7 is an irrational number? 
20150607 

From Sayak: Is 22/7 is an irrational number Answered by Penny Nom. 





A two digit number 
20150605 

From Madison: Trini took some photos. The number of photos she took is a two digit number.
The sum of the digits is 11. The tens digit is 3 more than the ones digit.
How many photos did Trini take? Answered by Penny Nom. 





The game of 24 
20150328 

From Suzanne: I love this game! Cannot figure out 4,9,10,16 to equal 24? Help! Answered by Penny Nom and Claude Tardif. 





8 golfers playing in 2x2 balls in 5 games 
20150318 

From Brian: We are 8 golfers who will be playing in 2x2 balls in 5 games.
is there a formula to minimize the chances of playing with a partner or opponent
too often please ? Answered by Victoria West. 





The game of 24 
20150121 

From aaron: 24 game whants me to use 11 14 5 and 9 to make 24 allowed (+  dividing and multiplying) 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. 





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. 





Solve sin3x = cos2x 
20140714 

From Emanuel: If sin3x=cos2x, find the value of x when x<0<90' Answered by Penny Nom. 





Sharing in the ratio of of 2:3:5 
20140711 

From Muzdalfah: Amount of Tsh 12,000 is to be shared among John,Hidaya and sabrina in the ratio of
of 2:3:5 respectivly.How will each get? Answered by Penny Nom. 





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. 





20 teams and 10 competition stations 
20140604 

From Joel: I have 20 teams. There are 10 competition stations.
Each station will accommodate exactly 2 teams to compete with each other at a time.
Each of the 20 teams needs to compete at each of the 10 stations exactly one time.
Here's the catch I cannot solve: how to schedule it so that each team plays EVERY OTHER TEAM once and only once, while never repeating a station. 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. 





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 with 3 teams of 20 
20140421 

From Joshua: Thank in advance for this great service
Golf  new  3 teams of 20  to create 20 unique groups of 3
For example use 3 teams of 3
1a 2a 3a
1b 2b 3b
1c 2c 3c
So groups are
1a 1b 1c
2a 2b 2c
3a 3b 3c
Groups can only have one a, one and one c  and that combo should be unique Answered by Victoria West. 





A 22 team golf league 
20140421 

From Terry: We have a team league at our local golf course.
We have 22 teams, we would like it so that each team plays the other team only once.
I have tried the scenario.
1,21;2,20;3,19;4,18;5,17;6,16;7,15;8,14;9,13;10,11;12,X X+1=1 scenario
2, 1;3,21;4,20,5,19,6,18;7,17;8,16;9,15;10,14;11,13;1,X
using formula from other post in your forums.
I can get all the possible playing arrangements. The big quandary is setting up the schedule
so that each week, each team would start on a different hole.
I can get the first 11 weeks scheduled very easily, it is just trying to get the last 11 weeks scheduled?
Any help would be greatly appreciated. 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 with 20 players over 17 weeks 
20140412 

From Chris: I have a golf league 20 players and 17 weeks. We don't have teams so I just want to have everyone to play with each other the about same number of time and, hopefully, randomly distributed throughout the season. We have had situations in the past where two people play together for three weeks in a row and then not anymore for the rest of the season. From other posts, I see how to schedule the first 5 weeks without repeats but I can’t figure out an algorithm to for the rest of the season. Thanks! Answered by Victoria West. 





Golf with 20 players and one compulsory bye 
20140331 

From Wayne: I'm trying to run an event with 20 players, I would like if at all possible to limit amount of people playing repetitively together. (Mix it up and play with different people). Here's the conditions. I want groups of 4 over 5 rounds. On each round I want 4 players to drop out and have a bye (to help run the game) but I dont want them helping a group they've played in if I can help it. Is this possible ? 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. 





24 golfers playing 3 rounds 
20140310 

From Jim: How can I rotate 24 golfers playing 3 rounds of golf so that none of them play with the same person twice. 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. 





The graph of f(x)=x^24 
20140207 

From Allison: Graph f(x)=x^24 and give the five point of the x/y intercepts. Answered by Penny Nom. 





Counting in base five using words not digits 
20140125 

From Randy: We all know how to count (in the base 10/decimal system) using words not numbers. For example: one, two, three, four, five, six, seven, eight, etc. However, in base 5 (for example) how would you count (in words). For sure  in base 5 the number 1 could be "one", the number 2 could be "two". However there seems to be no words to describe base 5 numbers beyond 0,1,2,3 and 4 (and perhaps 10). In base 5 the number 10 is not ten. Rather it is "five". In base 5 what word(s) describe numbers larger than 10? What words are used for 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 44,...etc. Also, consider a man and woman were married in the Gregorian year 1964. If they had an anniversary tomorrow  how long would you say they've been married in base 5 speak? In numbers their Golden Anniversary would note 200 years of marriage in base 5. How would you articulate their years together in base 5? I don't recall seeing verbiage to represent numbers in any system other than the decimal/base 10 system. Do such things exist for other systems? Answered by Harley Weston. 





A schedule for 32 golfers 
20131122 

From Scott: I would like a schedule for 32 guys playing in 8 foursomes for 13 week. I would like it so that no one plays in the same foursome more than once or twice. Is this possible to do??? Can you let me know at bogeysm@yahoo.com if you can do it and if you will do it. Answered by Victoria West. 





Two teams of 4 playing 4 rounds of golf 
20130929 

From Tom: We would like to play a ryder cup format with two teams of 4 playing 4 rounds of golf. Three of the rounds would be pairs playing each other and one round would be singles. How can we set up the foursomes so we balance the number of times we play with every other golfer. Answered by Victoria West. 





A schedule for 2, 7 team divisions 
20130924 

From Sampson: I'm looking to set up a weekly schedule within a 22 week segment of 2 7 team divisions where every team plays every other team in their divison 3 times and have 4 cross over games with 4 of the other 7 teams in the other division. I've yet to figure this out.
Thanks for your time. Answered by Victoria West. 





Two, 2digit numbers 
20130924 

From Tony: Write a problem that has two 2digit numbers.
solve your problem. Answered by Penny Nom. 





A two digit number 
20130904 

From JEFFERSON: The sum of the digits is 6. When the digits are interchange, the new number represented is 3 time the 10 digit of the original number. Find the original number? Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





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. 





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. 





A 2digit number 
20130513 

From A teacher: Find a “2digit number” where the sum of the 1st digit (on the Left)
and the square of the 2nd digit equal the same number. Answered by Lorraine Dame, Harley Weston. 





20 golfers over 5 days 
20130509 

From Russ: we have 20 golfers over 5 days, with 4 people per foursome which makes 5 groups each day. I would like to each person to play with everyone at least once if possible. Do you have a formula for this? Answered by Victoria West. 





25% 
20130328 

From aaliyah: what is the raw data of 25% Answered by Penny Nom. 





Multiplication in base two 
20130201 

From Michael: multiply in the indicated base
110two*11two Answered by Penny Nom. 





Plotting y=f(x)+2 
20130121 

From Gavin: how would you plot y=f(x)+2 Answered by Penny Nom. 





Some 6 digit numbers 
20121023 

From Mason: How many different 6 digit numbers can you make using the digits 1 ,2 5, 6, 7, and 9? How many of these sixdigit numbers are divisible by 6? Answered by Penny Nom. 





A 2 acre plot 
20121022 

From bob: If a plot of land on the south side is 290.16 feet wide, how many feet on the west and east side to the north to make a 2 acre plot?
Thank You Bob Answered by Penny Nom. 





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. 





Adding more than 2 fractions 
20120910 

From Anonymous: How do you add or subtract more than 2 integer fractions?
OK, here is an example.
5/6 + 7/4 + 13/8
Please tell me the steps.
Thanks grade 9 student Answered by Robert Dawson and Penny Nom. 





Golf for 20, two teams of 10 
20120830 

From Mark: Hi
I have to teams of 10 people playing Ryder cup format(against each other)
Can I have all 20 people playing with someone different over 3rounds of golf while remaining on there respective team I.e. players 1 to 10 must team up with a player of that group against a pair for players 11 to 20
I hope you can solve this for me
Thanks a bunch Mark 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 2digit number 
20120823 

From patty: Write the 2digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is Answered by Penny Nom. 





Drawing cards from a standard 52card deck 
20120707 

From Fatima: My daughter has to complete the project in probability chapter.Her gave her a complete probability chapter and told her to do all the problems.Out of them some questions I am not getting
The question is like this please give me a detailed explanation.
When drawing cards without replacement from a standard 52card deck, find the maximum number of cards you could possibly draw and still get
a. fewer than three black cards
b. fewer than six spades
c. fewer than four face cards
d.fewer than two kings Answered by Penny Nom. 





A cylinder is to be filled with peas. 
20120612 

From Silje: Hi! How can I solve the following question without the use of a calculator?
"A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on.
This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?" Answered by Robert Dawson. 





29 golfers 
20120604 

From robert: i have 29 golfers and have to make 8 teams for a golf scramble there will be 5 teams of 4 and 3 teams of 3 what is the fairest way to make up the teams? Answered by Victoria West. 





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. 





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. 





A golf league with 2 man teams 
20120411 

From Cosmo: wanting to set up a golf league with 2 man teams. There are 14 A players and 14 B players.We want each A player to team with each B player once and each A player to play against each other A player once.Is this possible Answered by Victoria West. 





Golf for 28 
20120410 

From EARL: HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR
5 DIFFERENT DAYS THERE WILL BE 7 GROUPS OF
4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO
PLAY WITH ONE ANOTHER ONCE AND NOT PLAY
WITH EACH MORE THAN ONCE IF POSSIBLE OR LIMIT
THE TIMES A GOLFER PLAYS WITH ANOTHER TO A
MINIMUM IF POSSIBLE. (PLEASE SEND AN EXAMPLE
OF THE SCHEDULING OF THE GROUPS FOR THE TEE
OFF ORDER)
THANKS FOR ANY SOLUTIONS YOU CAN PROVIDE.
EARL Answered by Robert Dawson. 





240 acres 
20120217 

From jon: How many linear feet are in a 240 acre rectangle piece of property Answered by Harley Weston. 





4 x 2 
20110830 

From Lucjan: how to sketch a diagram that shows 4x2 expression? Answered by Penny Nom. 





25 billion dollars 
20110826 

From Bill: If you have $25billion dollars, what would the value of this amount become if you inflated it at 4% per year for 55 years?=C2=A0 My TVM calculator will not go this high. Answered by Penny Nom. 





A two digit number 
20110826 

From Felicia: Write the 2digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit.
Zero is not one of my digits Answered by Penny Nom. 





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 rational number 
20110517 

From owais: according to definition of irrational number "a number which cannot be
expressed in p/q form is called irrational number"
square root of 2 is a irrational number but if i round off the digit correct
to two decimal places so it becomes 1.41 and we can easily convert
into p/q form so it is a rational number ??? Answered by Penny Nom. 





The game of 24 
20110506 

From shaylin: how do you use 3,9,7,9 once in any operation equal to 24? Answered by Penny Nom. 





20 acres, 12 inches deep 
20110224 

From David: How many linear yards of material is needed for a square plot of 20 acres by 12 inches deep? 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. 





22 people playing 6 rounds of golf 
20110131 

From angi: I'm having a problem scheduling matches for a golf vacation.
We have 22 people playing 6 rounds of golf.
We know that we will need to have two 3 man pairings each day.
Is there a way to make sure that is not a great deal of duplication.
I did see how Penny answered a question in 2005 with the circles.
Is there a way mathematically to do this or through excel? Answered by Victoria West. 





The game of 24 
20101026 

From gabrielle: What is the answer using the numbers 0 0 0 0 (trig and calc are
allowed, all math is allowed) in the game 24? Answered by Claude Tardif. 





a^(2^n) 
20101022 

From Tim: I am trying to understand a^(2^n).
The hint they give is a^(2^(n+1)) = (a^(2^n))^2
I am writing a program that will solve a^(2^n) recursively but need to
understand the power before I begin.
I am currently pursuing writing (a) x (a^(2^(n1))) where the
(a^(2^(n1))) would be the recursive function call a n approaches 0.
Once n is 0, the result would be multiplied by a two more times.
Anyway, explaining these powers would be appreciated. I will most likely
complete the program before the answer but I want to understand the
logic of these powers. Thank you, Tim Answered by Stephen La Rocque. 





What is 2^2? 
20100825 

From alex: I know that (2)^2 is 4 but what is 2^2? Answered by Robert Dawson and Penny Nom. 





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. 





The game of 24 
20100220 

From haley: hello.... we have these very hard make 24 stumpers. i am stuck on one.... how can you make 24 using the numbers 771318?? thanks! Answered by Claude Tardif. 





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. 





A cylinder is cut at an angle of 20 degrees 
20100125 

From sanjay: If I have a cylinder with 40mm diameter and I will cut it at an angle
20 degrees so what would be the increased radius or dia.??? of the cylinder Answered by Penny Nom. 





Two percent 
20091220 

From Brian: Hello I am having a problem figuring out something. Someone told me that .98 is the same as 2% how is this possible, how did they figure this out
here is my example 929.79 x .98 = 911.19, is the same as 929.79 x 2% = 18.59, now minus the 18.59 and you will end up with 911.19, how did they convert 2%
to .98, please help thgis is driving me nuts as I am not very good at math. Thank you
Warmest Regards
Brian Answered by Penny Nom. 





Two digit numbers 
20091210 

From Jim: Can you tell me how many 2 digit numbers can be created
from the following:
1118539 Answered by Penny Nom. 





Game of 24 
20091209 

From Tony: Checked out all of the previous inquiries into the crazed game, and found none with these particular numbers: 1, 4, 6, 7. I've tried every method I can think of, please Help! Tks. Answered by Robert Dawson, Penny Nom and Claude tardif. 





The graph of f(x2) 
20091119 

From Kapilan: Hi please answer the following question:
Given the function f(x)=x^2 sketch the graph of f(x2) Answered by Robert Dawson. 





Integration of cos (x^2) dx 
20091012 

From Venkat: How do you evaluate the integration of cos (x^2) dx ? Answered by Harley Weston. 





24 golfers, 6 days 
20091003 

From patrick: i need a pairing schedule for 24 golfers for six days playing in foursomes. Please Answered by Victoria West. 





Game of 24 
20091002 

From trami: game of 24 by using 4 7 7 1? Answered by Claude Tardif. 





24 golfers 
20091001 

From Peter: I am working on a 19 week golf schedule with 24 golfers, and I would like to know how to make up six foursomes each week without having a player paired with the same golfers. Answered by Victoria West. 





Game of 24 
20090924 

From vanessa: Using the following numbers 13,6,6, and 12 to equal 24. Using 5th grade math Answered by Penny Nom and Claude Tardif. 





24 golfers: 4 days 
20090921 

From Steven: We have 24 golfers (6 A's, 6 B's, 6 C's & 6 D's) playing 4 days.
Each day a foursome consist of an A, a B, a C & a D player.
Can you give me a pairing list so that no two golfers will play on the same foursome for the 4 days? Answered by Chris Fisher and Victoria West. 





The game of 24 
20090827 

From ANITA: Help I'm suppose to be a math expert, yet I can not yield 24 from the numbers 8,4,9,9, using each only once. HELP Answered by Penny Nom. 





The game of 24 
20090826 

From melvi: how can you get the numbner 24 but only useing the numbers 7,5,4,5 Answered by Penny Nom. 





Fact families 
20090824 

From Camasha: I am trying to help my daughter with fact families. I understand the premise from your previous explanation on the site . Generally when applying addition and subtraction their are two add and two subtraction utilizing all three numbers. However what do you do when you have a series like like 9, 9, 18 Answered by Penny Nom. 





root 2 is irrational 
20090731 

From prateet: prove that root2 is an irrational number. Answered by Robert Dawson. 





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. 





Game of 24 
20090522 

From Sam: Using the numbers 7, 3, 2, and 2, how do you get the number 24? Answered by Claude Tardif and Harley Weston. 





28 teams 14 lanes , 9 weeks no repeats 
20090519 

From paul: 28 teams 14 lanes , 9 weeks no repeats Answered by Karen Meagher. 





Game of 24 
20090502 

From Barbara: using the numbers 1,3 7 and 9 only once how do you get the answer of 24 Answered by Claude Tardif. 





28 golfers 
20090418 

From DON: HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR 24 DIFFERENT DAYS
THERE WILL BE 7 GROUPS OF 4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO PLAY WITH ONE
ANOTHER AS EVEN AS POSSIBLE (SAY 2 TO 4 TIMES EACH OVER THE 24 DAYS)...THANKS DON Answered by Victoria West. 





Game of 24 
20090408 

From Joe: How do you get 24 using 6,9,10,10 once. Its called the 24 game.
Joe Answered by Harley Weston. 





Game of 24 
20090405 

From Ramona: math 24 using 16, 9, 20, 7 Answered by Penny Nom. 





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. 





The game of 24 
20090301 

From Jeff: My son in the 5th grade was given a problem for extra credit and could use parents help. He was given the numbers 21, 13, 9, 6 and asked to use each number only once by +, , /, x the numbers in any order to obtain an answer of 24. Answered by Harley Weston. 





Collecting an army 
20090225 

From bevaz: Question from bevaz, a student:
A ruler orders his chamberlain to collect an army from 30 houses. The servant goes to the first house alone and collects one man. At each house after that he takes the same number of men as he has already collected, so at the second house he goes with one other and so on. How many men did he collect in all? Answered by Penny Nom. 





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. 





The substitution method 
20090206 

From amber: Pleasse help me with this problem
x+y=2
y2x=1 Answered by Penny Nom. 





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. 





20 of us golf together in groups of 4 
20090124 

From D.: Every Sunday, 20 of us golf together in groups of 4. I am looking for a
way that each of us play with 3 other people each week and ultimately get
to play in groups that are unique. For instance if week 1, I play with 2, 3, 4
and then the next week I play with 5, 6, 7, and the 3rd week I play with 8,
9, 10 and so forth until I have played with everyone. Everbody else should be
doing the same thing. Can you give me a schedule for this and how many weeks
would it take for all of us to accomplish this where we all play with different
combinations of people. (We should not play with the same person very often or even
the same pairs of people but everyone should play with everybody else) I hope
this makes sense........whew and thanks! 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. 





24 golfers playing golf for 9 rounds 
20081223 

From Duane: Got 24 golfers playing golf for 9 rounds. Any formula where everyone can play with everyone else at least once. We are playing 4somes only. Thanks, Duane Answered by Victoria West. 





Golf  24 guys 4somes 6 rounds 
20081207 

From Duane: Thank you. What about 24 guys 4somes 6 rounds everyone playing with each
other at least once.
Thanks again.
Duane Answered by Victoria West. 





Combinations of Golf Groups 
20081205 

From Duane: We have a golf outing coming up with 25 golfers playing 5 rounds in 5somes. Is there a formula to figure out where everyone can play with different people each round? Thanks, Duane Answered by Victoria West. 





A log base 2 problem 
20081126 

From dave: solve for x
(log base 2 of x)  (log base 2 of (x2)) = 3 Answered by Penny Nom. 





The game of 24 
20081124 

From Davey: this has us all stumped. 5 ,5 ,7 ,and9 = 24. Oh may you assist in ending
our brain pain Answered by Penny Nom. 





Sec(2x) 
20081123 

From Evan: Prove that this is an identity...
sec2x = sec^2x / 2  sec^2x Answered by Harley Weston. 





Arrays of 72 marbles 
20081113 

From natalie: draw four possible arrays for 72 marbles Answered by Penny Nom. 





Filling a tank with 2 taps 
20081110 

From Murray: 2 taps turned on together can fill a tank in 15 minutes. By themselves, one
takes 16 minutes longer than the other to fill the tank.Find the time taken to
fill the tank by each tap on it's own. Answered by Penny Nom and Victoria West. 





Bags of pennies 
20081011 

From paul: jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag? Answered by Penny Nom and Victoria West. 





The nth term of a sequence 
20080913 

From lavett: what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4... Answered by Stephen La Rocque. 





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. 





20 golfers playing 5 rounds in 4somes 
20080903 

From joe: 20 golfers playing 5 rounds in 4somes. 5 players in group A play with all 15 golfers in groups B,C,D but not with any in their own group (A).
5 players in group B play with all 15 players in groups A,C,D but not with any in their own group (B) and so on. So each 4some has an A,B,C,&D player each of the 5 rounds. Answered by Chris Fisher. 





Four weights 
20080825 

From Darla: A balance had known weights of 1/2 lb, 1/4 lb, 1/8 lb, and 1 oz. Edna's object weighted 2 oz. more than Paul's. Each used 3 known weights to weight his or her object. which know weights did each use? Answered by Penny Nom. 





The game of 24 
20080820 

From Tasha: I have four numbers a 6, a 6 a 5 and a 3, i can add subtract divide or multiply these numbers in anyway but i have to use all of them and call only use them once i have to come up with a total of 24 Answered by Penny Nom. 





Does the sequence 1 2 4 8 16 32 etc have a name? 
20080717 

From Richard: Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name? Answered by Victoria West. 





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 number that ends with 2 
20080623 

From Jim: A number ends in 2. If you were to place that digit at the beginning of the
number, the resulting number will be twice the original. Find the smallest
such number. Answered by Stephen La Rocque. 





The game of 24 
20080410 

From sherwin: ok is like this you must get 24 using 1,5,5,5 but you can only use +,  , / and * Answered by Claude Tardif. 





The game of 24 
20080401 

From Frank: Hi, my name is Frank. I have been really stumped on this 24card. It has the 4 # of 21,3,5,10. If you have any suggestions, I would be grateful! Answered by Claude Tardif. 





Twenty golfers 
20080316 

From john: I have a group of 20 golfers. We plan on playing 6 rounds of golf in 4 days. I would like to have the most possible combinations of players without each player playing with anyone if possible, in the 4 days of golf Answered by Victoria West. 





The game of 24 
20080206 

From Jameeka: What is a solution for 10,11,9 and 2 (Using fractions) in the game 24 square. Answered by Penny Nom. 





A 24 hour clock 
20080131 

From CARLA: at a certain time i looked at a 24hour digital clock and noticed some things about the time. (1 The number in the hours section plus the number in the minutes section makes 60.(2 One of the digits in the minutes section is the square root of the other digit in the minutes section.(3 The sum of the digits in the minutes section is the number in the hours section reversed. what is the time? Answered by Penny Nom. 





1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 
20080122 

From Neil: Find the next two terms in the following number sequence
1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128
Find a general rule for the nth term of the sequence Answered by Penny Nom. 





The game of 24 
20080117 

From Raina: I have four numbers 3 3 9 5 that need to equal 24 using addition subtraction multipliction and division and I'm so stuck. Answered by Chris Langdon, Stephen La Rocque and Claude Tardif. 





For how many positive integers n is n^2 + 96 is a perfect square? 
20071218 

From Rajesh: For how many positive integers n is n^2 + 96 is a perfect square ? Answered by Penny Nom. 





sin^2x=1/2(1cos2x) 
20071212 

From katelyne: Hello there.. I was assigned a problem that I am having trouble with in my
PreCalc class and it is as follows:
sin^2x=1/2(1cos2x) Answered by Penny Nom. 





How many marshmallows did I use? 
20071121 

From gloria: the # of marshmallows i use is an even # .it is 2 digit number more than 10 less than 20 the 10th digit half of one digit.how many marshmallows did I use? Answered by Chris Langdon. 





The game of 24 
20071119 

From M: Please help...how would you compute 2,2, 6, and 9 to equal 24? Answered by Penny Nom. 





The game of 24 
20071117 

From Todd: Hello. My son is very good at the Math 24 game and when he is stumped,
I am usually able to figure it out. However, we are both stumped with
this one. The numbers are 6, 6, 9 and 5. You can use addition, subtraction,
division and multiplication. Please help us equal 24 with those 4 numbers. Answered by Claude Tardif. 





Paying with silver  Part 2 
20071017 

From Shanna: The paying with silver problem. I understand how to do the problem, but could you please explain how you would use base 2 arithmetic to solve it. Answered by Penny Nom. 





Golf pairings 
20071002 

From Mike: Regarding arranging golf players so no person plays with anyone more than once.
You have given examples for 16 and 24 players. If it can be done, i need a
solution for 20 players, 4 players per team one round per day for 5 days Answered by Victoria West. 





The game of 24 
20070927 

From Amanda: I'm really stumped on a 24 math game question from math class. The numbers are 7,11,17,and 20. Help?? Answered by Claude Tardif. 





Making dot arrays 
20070905 

From angela: What do we call the numbers that cannot be arranged into 2row arrays? Answered by Penny Nom. 





Four fours 
20070823 

From Belinda: My son came home with a math question that I can figure out. He needs to use only the number 4 and only four 4's, no less no more.
The problems need the answers 11,13,14,and 18. He can use any mathematical sign except square root. He's been able to get all but these
so far and I've worked them, but can't come up with the problems. Can anyone help? Answered by Stephen la Rocque. 





Log base 2 of log base 2 of x 
20070627 

From alex: y = log base 2 of lag base 2 of x
The slope of the tangent to the given curve at its xintercept is..? Answered by 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. 





24 Game: 7, 5, 3, 3 
20070611 

From Natasha: In the maths game called '24', how can you solve 7, 5, 3, 3?
I like playing a maths game called '24'. Answered by Stephen La Rocque. 





Game of 24 
20070404 

From teri: How do you find the answer of 24 by using 12,24,7 and 2 only once. Answered by Stephen La Rocque. 





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. 





The game of 24 
20070322 

From Britney: I have a math problem with the game 24. I am not sure how to solve it.
You can use +, , multiplication, division, ( ), square root, and exponents.
Please help me. The numbers are 1, 6, 7 and 8. You have to use all the
numbers and you can only use them once. Answered by Penny Nom. 





28 golfers playing golf over 7 days 
20070320 

From ian: I have 28 golfers playing golf over 7 days
I would like everybody to play with each other at least once
Is there a schedule?
Thank you
Ian Answered by Penny Nom. 





The game of 24 
20070309 

From colleen: We are playing the 24 math game where four numbers need to combine using any sign (+,  X, \) to equal 24. The four numbers are 22, 21, 6, 20. Answered by Penny Nom. 





Game 24 
20070209 

From Becka: I need help figuring out this sequence for 24 2 2 3 5 Please help Answered by Steve La Rocque, Penny Nom, Claude Tardif. 





The game of 24 
20061128 

From John: Math 24 with 9, 8, 4, 2? Answered by Stephen La Rocque and Penny Nom. 





A problem involving logs 
20061126 

From Beth: any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!!
log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4 Answered by Stephen La Rocque and Penny Nom. 





Arithmetic with base 2 
20061126 

From Yuva: can we do arithmetic ,base 2. If yes, how and if not, why. Answered by Stephen La Rocque. 





2row arrays 
20060906 

From Liz & Samantha: What do you call the numbers that cannot be arranged into 2row arrays? Answered by Penny Nom. 





A golf schedule for three days 
20060818 

From Jon:
I was wondering if I could trouble you to assist me with the following: I am working on a playing schedule for 28 golfers. 7 groups of 4. I have 3 golf days to schedule.
Ideally, I would like to schedule all 28 golfers in 7 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible? Answered by Penny Nom. 





How many digits are in the number 2^64? 
20060614 

From Trang: How many digits are in the number 2^{64}? Answered by Stephen La Rocque. 





Twenty golfers 
20060508 

From Mona: We have twenty golfers and four rounds of golf. We would like to figure out how to make foursomes so that each golfer plays with as many different golfers as possible. Answered by Penny Nom. 





More on the game of 24 
20060505 

From Kathy's daughter: My daughter's 5th grade class plays the 24 math game. She came home
the other day with a real stumper! The numbers on the card are 5,5,2,and 6.
The rules say you must use every number,you may only use a number once,you
can only add, subtract, multiply and/or divide and the answer is 24. Can you
help!!!! No one where I work has been able to figure this one. Answered by Paul Betts and Penny Nom. 





9, 8, 7 and 2 in the game of 24 
20060317 

From Alana: I just began student teaching in a 5th grade math class and found that the students play 24 in class, a game that I used to play in elementary school. The students choose a card which shows 4 numbers and then have to use any combination of addition, subtraction, multiplication, and division to reach 24. There was one card that we found that seems to have all of us stumped. The four numbers are 9, 8, 7 and 2. Can you figure out how to make 24 with those? Thanks so much for your help! Answered by Claude Tardif. 





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. 





More on the game of 24 
20060202 

From Cathy: 10,16,9,4 this numbers have to equal up to 24. we can't figure it out. Answered by Claude Tardif. 





The game of 24 with 7, 5, 5 and 4 
20051218 

From Nicole: i was playing the 24 game the other day. you get 4 digits and you have to turn them into 24. You can use addition, subtraction, division, and multiplication. You have to use all the numbers but you can only use each number once. an example is 2 4 4 1 the answer is (2x4)(41)=24. I got stuck on one. The numbers were 7 5 5 4 . Answered by Penny Nom. 





Four 25sided dice 
20051124 

From dan: Simply put, I am curious to find the likelyhood of each possibility (4100) if I were to roll 4 25sided die. It seems to start off simply, as 1, 4, 10, 20...following the inside diagonal of Pascal's triangle. But as soon as i reach the point where the sum is greater than the number of sides, Pascal's no longer seems to work. I would be greatly appreciated if I could be informed of the proper formula to find this answer, or perhaps if my theory of doing it is wrong. Answered by Andrei Volodin and Shaun Fallat. 





The game of 24 
20051010 

From Kim and Chris: My 4th grade son came home with a math game called 24 game. In it each card has 4 numbers on it. Each number can only be used once, in any order, using multiplication, subtraction, division, or addition. We are stuck on one and wondered if you could help. The four numbers are: 9, 9, 9, 9. And they must equal 24. Any clues? Answered by Claude Tardif. 





cos x * cos 2x * cos 4x * cos 8x 
20050829 

From Leandro:
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Answered by Chris Fisher and Penny Nom. 





The value of n*tan*(180/n) tends to pi 
20050711 

From Daniel: I am 14 and i have been given a piece of maths coursework whereby a farmer has to fence off a piece of land as large as possible using 1000m of fence. I already know that the formula for working out the area of any shape of a 1000m perimeter = 500^{2}/ n*tan*(180/n), however, after some research I have found out that as the number of sides (n), tends to infinity, the n*tan*(180/n) tends to pi. Why is this? Answered by Penny Nom. 





The game of 24 
20050110 

From Manny: HI  my daughter and I are being driven crazy by the following "24" question 7,7,3,3. She's good at the game (well, better than I am) and her teacher gave her this one. Any insight would be appreciated! Answered by Claude Tardif. 





20 Golfers 
20041026 

From Ian: I have 20 golfers playing over 6 days I would like to schedule all 20 golfers in 5 groups of 4 on each day here is the catch.... I would like each player to play with each other once during the 6 days. Answered by Chris Fisher. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





The game of 24 
20040916 

From Angelica: how can you make 24 out of 7,7,6,5? Answered by Claude Tardif. 





The game of 24 
20040914 

From Alan: I was playing that math 24 game and i cant get 21,14,2,2 to equal 24 Answered by Claude Tardif. 





The 24 game 
20040909 

From Erik: Ive spent around 40 hours on this one problem. I need help. 3,3,7,7 Answered by Claide Tardif. 





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 game of 24 
20040604 

From Samantha: i have the game 24 (the one where you have to use multiplication, division, addition, and subtraction to get to the answer 24) I was playing when i came across the 4 numbers 20, 17, 7, 11 and i cant seem to get 24. 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. 





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. 





1 + 1 = 10 
20030917 

From David: could you please explain to me how 1+1=10 thanks Answered by Penny Nom. 





The game of 24 
20030903 

From A student: We have a game where four numbers must equal 24 using addition, subtraction, multiplication and/or division.Ý I am stuck on the following four numbers  12, 24, 9 and 17. Answered by Penny Nom. 





The units digit of 57 to the 28th power 
20030901 

From Maria:
If 57 is raised to the 28th power, what must be the units digit in the result? If you raise 7 to the 500th power, what is the numeral that will appear in the units digit position? 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. 





2/sqrt(2) 
20030507 

From Mike: I was looking at an example of csc 45 deg where csc = hyp / opp = 1 / (sqrt(2) / 2) = 2 / sqrt(2) = sqrt(2) I just don't get this. If sqrt(2) = 1.4142145..... How can 2 / sqrt(2) = sqrt(2) as the example shows? Answered by Penny Nom. 





Can twice a square be a square? 
20030325 

From Mike: The other day it occurred to some students that they could think of no square number which is an integer, which can be divided into two equal square numbers which are intergers, Or put another way, no squared integer when doubled can equal another square integer. For example 5 squared plus 5 squared is 50, but 50 is not a square number. Answered by Walter Whiteley and Claude Tardif. 





Two modes 
20021212 

From ali: I have a math assignment to pick the mode in a set of data. 12 and 21 both appear twice in the data set. What is the mode? Answered by Penny Nom. 





Constructing a tangent to two circles 
20021128 

From Tom: I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Answered by Chris Fisher and Penny Nom. 





The 24 game 
20021116 

From Michael: Hello, my name is Michael and I am in elementary school .. We have a game we play in math class called 24 game. In it each card has 4 numbers on it. Each number can only be used once, in any order, using multiplication, subtraction, division, or addition. We are stuck on one and wondered if you could help. The four numbers are 109164. And they must equal 24. Any clues? Answered by Penny Nom. 





The repetition of doing many straight forward problems 
20021016 

From Dan: I am the father of a very bright 9 year old girl. She is very interested in math and she grasps concepts very quickly. I am concerned that she may become bored with the repetition of doing many straight forward problems. Her current math teacher has her working in a challenging math book and she is doing 3+ digit multiplication. She misses 2 or 3 out of ten of these problems due to simple addition errors. Should she continue to practice these problems until she can get them all correct? Or, should she move on? Answered by Kathy Nolan and Claude Tardif. 





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. 





The number of decimal places in 1 over a power of 2 
20020912 

From Allan: Does anyone notice that the maximum number of decimal place of the number 2 dividing 1 and its increment (4, 8, 16...etc) is the same as the power of number 2? eg. 2^{2}=4, thus the max number of decimal of ^{1}/_{4}=0.25 which is 2 decimal place and 2 is the number of power of 2 take 64 as example: 2^{6}=64, and take ^{1}/_{64}=0.015625 which has 6 decimal place (and is the power 6) Is there such a law in math? If yes, can you tell me what it is? Or is this my discovery? Answered by Paul Betts. 





The 20 kilometer walk 
20020820 

From A student: THE 1996 OLYMPIC GOLD METAL WINNER FOR THE 20 KILOMETER WALK WAS JEFERSON. HIS TIME WAS 1HOUR, 20 MIN,AND 7SECONDS. HIS TIME WAS NOT GOOD ENOUGH TO BEAT THE WINNER IN 1988 BY JOSEF. HIS TIME WAS 1 HOUR,19 MIN, 57 SECONDS. WHAT WAS THE WALKING RATE OF EACH PERSON? Answered by Penny Nom. 





A schedule for 24 golfers 
20020525 

From John: I am working on a schedule for 24 golfers. 6 groups of 4. I have 8 golf days (twice per week for a month). Ideally, I would like to schedule all 24 golfers in 6 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible? Answered by Chris Fisher. 





The square root of 2 
20020305 

From Roger: Does two (2) have a square root or do the numbers just keep going? Are there any other numbers that behave like two when it comes to extracting the square root? Answered by Penny Nom. 





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. 





Making 24 
20020117 

From Renee: My 4th grade daughter and I need to find a simple math sentence using 5, 5, 3, & 7 to equal 24. You can add, subtract, divide or multiple. Answered by Penny Nom. 





Papy's Computer 
20020111 

From MaryAnne: My secondgrade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8. Answered by Harley Weston. 





2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 
20011105 

From Cynthia: justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom. 





27 
20010910 

From Kacy: In class we were given this problem. We have the numbers 30, 29, 19,11,26. these numbers = 27 in some way but how? the numbers can be applied any way using +  / X ( ) but can only be used 1 time each. can you please help me. Answered by Claude Tardif. 





Some irrational numbers 
20010703 

From Kellie:
 Is it possible to write pi as a fraction?
 Is it possible to write the square root of 2 as a fraction.. Explain why?
Answered by Harley Weston. 





f(x), f(x) + 2, f(x +2) 
20010404 

From Monica: Could you explain to me how one should go about graphing functions such as f(x), f(x+2), and so on. Also, how should you explain things such as constants and relationships among functions? Answered by Penny Nom. 





Solve for two variables 
20010225 

From A student: How do I solve for %1 and %2 in the following formula when T1, T2 and T3 are known? %1 and %2 are ratios of the same element, therefore %1 + %2 = 100%
(%1 x T1) + (%2 x T2) = T3 Answered by Penny Nom. 





Find the two numbers 
20010221 

From A grade 6 student: Find the two numbers: 5 is a common factor; 100 is a common multiple; neither number is a mulitple of the other; both are even. Answered by Penny Nom. 





Math game 24 
20010221 

From Kristi: We have a game we play in math class called 24 game. In it each card has 4 numbers on it. Each number can only be used once, in any order, using multiplication, subtraction, division, or addition. We are stuck on one and wondered if you could help. The four numbers are: 3, 3, 5, 7. And they must equal 24. Any clues? Answered by Claude Tardif. 





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. 





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. 





Paying with silver 
20000426 

From Luther Jackson: A silver prospector is unable to pay his March rent in advance. He owned a bar of pure silver, 31 inches long, so he made the following arrangement with his landlady. He would cut the bar, he said into smaller pieces. On the first day of March he would give her and inch of the bar, and on each succeeding day he would add another inch to her amount of silver. She would keep this silver as security. At the end of the month, when the prospector expected to be able to pay his rent in full, she would return the pieces to him. . . . Answered by Claude Tardif and Penny Nom. 





2^32 + 1 
20000408 

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





Is a sheet of paper 2dimensional? 
20000306 

From Jaclyn Evans: One day, we were discussing 3dimensional items. Is a sheet of paper considered a 3dimensional shape? Or is it 2dimensional as described by 8.5 by 11 size? Also, could you give me an example of a 4dimensional item or scenario? Answered by Harley Weston. 





2 to the x and x squared 
19990917 

From John: For what values of x is 2 to the exponent x greater than x squared? Answered by Harely Weston. 





2,5,8,1 yields 24 
19990912 

From Terry Hill: I was wondering how do I make the numbers 2,5,8,and 1 equal 24? Answered by Penny Nom. 





Y2K? 
19990903 

From Mike Putzakulish: In Y2K, the "K" stands for thousand, but where did the "K" come from? I know it's not a Roman Numeral, but what is it?? Answered by Chris Fisher and Harley Weston. 





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. 





The square root of two is never supposed to end 
19990306 

From a wondering student: i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input. Answered by Jack LeSage and Penny Nom. 





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. 





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. 





Comment fait on pour justifier que... 
20020930 

From Lucie: Comment fait on pour justifier que p au carré est égal à 2 fois q au carré? Answered by Claude Tardif. 





Un polyedre ayant comme face 20 triangles 
20000802 

From Sonia: J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux. Answered by Chris Fisher. 

