







A 50:1 ratio in a pint 
20200522 

From Steve: How much oil do I need to put in a pint if it's 50:1 ratio Answered by Harley Weston. 





Is there an equation to find what percent of 0 is 1? 
20200309 

From Asher: Question: Is there an equation to find what percent of 0 is 1.
I remember learning quite a long time ago that the answer inst 0 and it isn't infinity. I'm pretty sure it was something like %=0 approaching infinity or %=1 approaching infinity. And I know it depends what value you assign the numbers i.e. dollars or temperature. Furthermore, is asking "what percent 1 dollar is of 0 dollars" the same question as "what percent profit do you make from selling something worth 0 dollars for 1 dollar."
Thank you for your time and consideration
Asher Answered by Penny Nom. 





30% profit 
20200220 

From Sidra: A car dealer bought a car for £7500 and sold it for 30% profit.
For how much did he sell the car? Answered by Penny Nom. 





Arranging 10 digits 
20191009 

From Laxmi: 1)The integers 0 to 9 are arranged along a straight line in some order.a) find a possible arrangement in which the sum of any three adjacent numbers is less than 15.b)is there an arrangement of this kind 0 is not included in the numbers. Answered by Penny Nom. 





400 in 7.5 billion 
20190828 

From Emma: What is a better way to express 400 in 7.5 billion?
My daughter has a rare condition, I want to know the answer to say “she is 1 in a ...” Answered by Penny Nom. 





Six digit numbers from 4 digits 
20190730 

From Tab: How many six digit combinations can be made from the numbers zero, two, five, eight? With repetition of numbers Answered by Penny Nom. 





One part in 10^x 
20190626 

From Jim: What is the meaning of the phrase ‘one part in 10x” where the x is an exponent? I have seen these examples: “...better than one part in 10x” and “...to within one part in 10x.” Answered by Penny Nom. 





The perimeter of 200 acres 
20190614 

From AARON: How many feet is the perimeter of 200 acres? Answered by Penny Nom. 





An 80 acre square 
20190511 

From Linda: How long and wide is an 80acre piece of land that is square?
How long and wide is a 160acre piece of land that is square? 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. 





A 4 sided lot 
20170815 

From Micheal: If one side of .4 acre is 25 feet what would the other three sides 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. 





A 40 acre square 
20170514 

From Richard: How many feet on each side of 40 acre square ? Answered by Penny Nom. 





A circle inscribed in a 30690 triangle 
20170407 

From Kameron: i have been given a problem with a 306090 triangle and a circle inscribed with a radius of 2 and was told to find the perimeter of the triangle 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. 





980 cubic yards of dirt 
20161217 

From Jondi: I am trying to visualize 980 cubic yards of dirt by using a metaphor.
Would this be the size of a car?
A fire engine?
A semitrailer?
How many trucks would you need to haul away 980 yards of dirt? Answered by Penny Nom. 





y = mx + c and Ax + By + C = 0 
20161018 

From Erick: please explain to me how to convert an equation from the form y=mx+c to Ax+By+C=o 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. 





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. 





0/0 
20160214 

From Noni: Q. 0÷0=1 Why it is wrong when 4÷4=1; 3÷3=1; 2÷2=1: 1÷1=1 ? 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 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. 





How can the probability be zero? 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Mathematics 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





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. 





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. 





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. 





What is 1000 billion billion? 
20150310 

From LeRoy: what does this mean? 1000 billion billion 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. 





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. 





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. 





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. 





The combination of 6 numbers from 1 to 355 that gives us 360 
20140529 

From Ion: Hi,
My name is Ion and I am trying to find the number of combinations of 6 numbers (angles) that would sum to 360 (degrees).
Thank you! Answered by Robert Dawson. 





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 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 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. 





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. 





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. 





8 numbers from 80 
20130904 

From susan: Out of 80 numbers how many combinations of 8 are there and what are they. Answered by Penny Nom. 





More than half of the people said... 
20130826 

From Lucy: Hi,
The question is:
Samoa 23%
Brazil 41%
Sri Lanka 52%
Senegal 39%
Armenia 37%
Croatia 20%
Why is the following statement true for the data above: More than half of the people said they were interested in Sri Lanka. The reason I don't understand the problem is that because the percentages add up to be greater than 100%, that means that the 500 people(as stated in the question) who participated in the survey got to pick more than once. Therefore, it is not 52% out of 100% anymore.
Thanks for taking the time to answer my question. Answered by Robert Dawson. 





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. 





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. 





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. 





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 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. 





Expanded exponential form? 
20120612 

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





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. 





240 acres 
20120217 

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





Expressing 0.5% 
20120206 

From Kenneth: Hello:
It is correct to express 0.5% as 5 tenths of one percent.
Is it also correct to express 0.5% as 5 tenths of onehundred percentage points or 5 tenths of one percentage point?
I think it would be 5 tenths of one percentage point because 5 tenths of onehundred percentage points would be 50 percentage points, but I'm not sure.
I thank you for your reply. Answered by Penny Nom. 





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. 





A group of 40 golfers 
20110711 

From Doug: We are a group of 40 golfers who play in 10 x foursomes playing 3 rounds. Can we all play with different players each round yet maintain the foursomes format. Answered by Victoria West. 





Construct a 30 degree angle 
20110610 

From Ella: they give you a simple straight line and ask you to construct an angle of 30 degrees at one end of the line using only a ruler and a compass? Answered by Penny Nom. 





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. 





A golf league of 60 golfers 
20110414 

From Keith: I have a golf league of 60 golfers and I want to have each golfer play in a different group of 4 each week for 24 weeks.
How can I do this Answered by Victoria West. 





What is x to the power of 0? 
20110323 

From Jason: What is x to the power of 0? Answered by Robert Dawson. 





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. 





10 golfer playing 5 rounds 
20110109 

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





The new diameter is 50 per cent larger than the original. 
20100904 

From mahwish: . A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased? Answered by Tyler Wood. 





Does 1= 0.9999....? 
20100407 

From Asia: Does 1= 0.9999....? There seems to be different opinions on this. Answered by Robert Dawson. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





An isosceles triangle 
20100211 

From Kim: I am given the length of the two legs of an isosceles triangle (8), and the base angles are 30 degrees...I am asked to find the area of the triangle with only this information Answered by Tyler Wood. 





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. 





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. 





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. 





30 students 
20090806 

From Peter: Question from Peter, a student:
Can you please help with the following questions?
(a) It is known that among any group of the three students in a class two of them are friends. Total number of students is 25. Prove that there is a student who has at least 12 friends.
(b) There are 30 students in a class. They sit at 15 double desks, each one is for two students. Half of the girls sit with boys. Is it possible to make a rearrangement so that half of the boys sit with girls? Answered by Penny Nom. 





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. 





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 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. 





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. 





0/0 
20090215 

From Justin: Hello, I was just wondering, what is the difference between 0/0 being represented as nullity or as an indeterminate form?
Justin Answered by Harley Weston. 





A 306090 triangle 
20090203 

From Inez: If you have a 306090 triangle and the only side you get is 73 and a 90 degree box, how do you find the area? Answered by Penny Nom. 





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. 





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. 





0.99999.... 
20080923 

From Eve: Hi, i had a problem with change 0.99999... this recurring decimal to a fraction. I know the method, but the answer I got is 1 as you can see below.
Where have i done wrong? Answered by Harley Weston. 





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. 





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. 





Zero divided by infinity 
20080503 

From ANNE: There was a question about what do you get when you divide Zero by infinity. There was an example using Potatoes. Could someone please explain a little bit more in detail, so that I can help my son who has Schizophrenia understand. He is big into Mathematics and is consumed by this question.
Thankyou so much,
Anne 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. 





A 306090 triangle 
20080416 

From Ron: 306090 triangle. Base is 2.75 how do I find the length of the other two sides? Answered by Penny Nom. 





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. 





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 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. 





Choosing 10 numbers from 40 numbers 
20080118 

From Antwan: I have 40 numbers........number 140.
I want to know how many times i can chose 10 of those numbers without picking the same exact sequence twice if its even possible? Answered by Stephen La Rocque. 





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. 





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. 





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. 





How can we explain to middle school students that 0^0=1? 
20061015 

From Peter: How can we explain to middle school students that 0^0=1? Answered by Steve La Rocque, Penny Nom, Claude Tardif and Harley Weston. 





a _________________ line forms a 90 degree angle with another line 
20060924 

From Lisa: a _________________ line forms a 90 degree angle with another line is this to it
what fills in the blank? first letter is E third letter is R and has 13 letters Answered by Stephen La Rocque. 





A base number raised to the power of 0 
20060824 

From Sheila: I'm a 5th grade teacher and need some help with a base number raised to the power of 0 always being 1. My kids asked me why and I told them I'd find out. Answered by Penny Nom. 





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. 





Interest computed on a 360 per year basis 
20060406 

From Sonya: Okay, I am reading this promissory note that says interest is computed on 365/360 basis by applying the ratio of annual interest rate (24%) over a year of 360 days.
I sure do not remember anything like this in school, and am stumped. Answered by Stephen La Rocque. 





A triangle of 50p pieces 
20060222 

From Stuart:
Ok, so i am collecting 50p pieces and arranging them on my desk in the shape of a triangle.
eg
50p
50p 50p
50p 50p 50p
50p 50p 50p 50p
I want to work out how much money I'm saving just by knowing how many rows of coins there are. If i can work out how many coins there are just by knowing how many rows I have I can just divide by 2 to find out the amount in dollars.
Answered by Penny Nom. 





Is a zero considered an even or odd number? 
20051213 

From Sylvia: Is a zero considered an even or odd number? Answered by Penny Nom. 





A 306090 triangle 
20050911 

From Gary: I have the length of only 1 side of triangle with angles of 306090 degrees. How can I find the length of the other 2 sides? Answered by Penny Nom. 





0.999..., asymptotes and infinity 
20041217 

From Mike: My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!! Answered by Claude Tardif and Harley Weston. 





A 306090 triangle 
20041109 

From Amy: How do you find the length of the hypotenuse of a 306090 triangle when the side opposite the 60 degree angle is 6 inches? Answered by Penny Nom. 





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. 





Zero to the zero 
20040918 

From Greta: My name is Greta, and I am a 7th grader and my test is coming up. The question I would like to ask you is why 0 elevated to 0 is unidentified. Answered by Penny. 





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. 





Zero 
20040212 

From Syazwan: can you tell me who and when the number zero was
discoveredd 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. 





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. 





0/0 
20030925 

From Thomas: How is 0/0 ever defined. 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. 





Positive, negative and zero 
20030904 

From Brian: Can the Value of zero be positive or can it be negative or can it be both. Answered by 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. 





Division by zero 
20030119 

From David: I've been to your site and am interested on the subject of division by 0. It's easy enough to give answers, but it's very hard, especially in this case, to make someone understand a mathematical problem. It's been about a year since my Calc class, and we never went over division by 0, only infinite numbers and such. My question is: How would you work a problem of (real number) / 0 ? As ignorant as it may sound to you, I am having trouble grasping this since I've only begun to understand some of it. Perhaps you could help. Answered by Harley Weston. 





Exponent 0 
20021002 

From Debbi: can you please tell me what the exponent 0 is (i.e. 7^{0}) Answered by Penny Nom. 





0.99999... 
20020926 

From Erica: Yesterday in my 8th grade math class we were being taught how to convert a Repeating Decimal into a fraction. Since I, for some odd reason, seem to understand math better than the rest of my classmates, i began to drown out my teachers explaination for the rule. While she was about half way through with explaining mixed decimals i came up with an unsolvable question. Like I said before, I understand how to turn a repeating decimal into a fraction, but how would I turn a repeating .9 into a fraction? We all know it would equal 9/9, but doesn't 9 over 9 also equal 1? Even though it comes very close to one, it never really equals one. I'm very confused about this and i would love it if you could clear this up for me. Answered by Penny Nom. 





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. 





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. 





F = 3 + 3 
20020319 

From Jessica: F= 3 + 3 WHAT IS F????? 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. 





50% 
20020115 

From Lakarrieh: 4 is 50% of what number? Answered by Penny Nom. 





450 students 
20011219 

From Jessie: My teacher told me that the number of ways of lining up the 450 students in our school is larger than the number of atoms in the universe. Is this right? This question came to Good Question, a regular feature on the CBC Morning Edition radio show in Saskatchewan. Answered by Denis Hanson and Harley Weston. 





Negative numbers 
20011115 

From Jewel: If zero means nothing or an empty set, then how can a number be less than zero, as in negative number? My understanding of negative numbers is distance from a set point in a given direction. Thus having a negative and positive side of a line is arbritary and is related to displacement rather than value. Am I in error? Answered by Penny Nom. 





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. 





60 seconds in a minute 
20011011 

From Andy: I am a fourth grade teacher. Yesterday my students asked "Why are there 60 seconds in a minute?" Which also led to 60 minutes in an hour? I have had trouble determining why the number 60? Any help would be appreciated. Answered by Penny Nom. 





Zero as an exponent 
20011004 

From Wendy: How do I explain to kids that i.e. 5 exponent 0 = 1? Does 0 exponent 0 = 1? Answered by Leeanne Boehm and Penny Nom. 





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. 





0.999999=1? 
20010906 

From Catherine: Hi! My teacher told us that 0.9 repeating equals one. We discussed how this is true. But, I was wondering if there is a proof that this is true. If so what is this called? I was trying to find information, but, it's hard when you don't know the name. Answered by Walter Whiteley. 





Repeating decimals 
20010421 

From Sarah: Hi, I'm working on a project for school. The theory I choose was "When turned into a fraction, a repeating decimal has a denometor that is a multiple of three." I have a couple of questions about this topic. My first question is, have you ever heard of this, and what can you tell me about it? My second question is, when I was testing this theory I came across .999... now, when this is a fraction it is 9/9 which is equal to one. The denometor is a multiple of 3, but it's a whole number. I don't understand how a decimal can be equal to a whole number since a decimal is a piece of a whole number. Please don't just show me a math problem, I don't want to see a math problem. I want to see an explanation of this theory and the decimal .999... Answered by Penny Nom. 





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. 





Why is 0! = 1? 
20010130 

From Diane: Every math book always claims that 1!=1 and 0!=1 are givens, and that we should just memorize it. i understand the 1! part, but where is the basis for claiming that 0!=1???? Answered by Walter Whiteley. 





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. 





10,000! 
20000721 

From Lauren: Hi I was just wondering if you could tell me how many zeros are in 100,000! (factorial.) Answered by Denis Hanson. 





A 100gon 
20000524 

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





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





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. 





.400 in Baseball 
19991215 

From Nieve Nielson: I have several questions to ask about the probability of getting a .400 in baseball:  What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times?
 What is the probability of a baseball player hitting a .400 in a season, considering that there are 100 games in a season? With the first two questions in mind:
 Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time?
Answered by Chris Fisher. 





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. 





Powers of zero 
19991031 

From Salina Young: Hello! I have two questions to ask about the power of "0". First, what is the value of "0' to the power of "0"? And why? Second, what is the value of "0" to the power of "2" or '3" etc? And why? Thank you for your help. Answered by Walter Whiteley and Harley Weston. 





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. 





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. 





Division by zero 
19990902 

From Joshua B. Mariano: Why can't I divide a number by zero. When I put in my calculater 0 divided by 7 it equals 0. But when I put 7 divided by zero my calculater say's error. Why can't this be solved? What is the answer? Is there a paper on it? Help? Answered by Walter Whiteley. 





Repeating decimals 
19990521 

From Stan: Hi, I am in Honors Math, and have confronted everyone, including teachers, about repeating decimals. What interests me is the number 0.9... and 1. Everyone says that since there is no number between 0.9...(repeating) and 1, that 0.9... = 1. However, isn't a repeating number a representation of a number, and not a real number? Let's look at it this way. 0.9 is close to 1. 0.99 is closer. 0.99999999999999 is even closer. so, 0.9... is a representation of it's closeness to 1. it's an active number... I don't understand how 0.9... is equal to 1. Please help me prove that 0.9... does NOT = 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. 





Finding Excluded Values 
19990401 

From Lorraine Le Cam: The question asks me to find the value of the variable that must be excluded in each rational expressionion. The operation is: a ______ a  2 How do I work this out? 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. 





Indeterminate forms 
19981211 

From R. Dixon: What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity. Answered by Walter Whiteley and Harley Weston. 





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. 





0! 
19970302 

From Donna D. Hall: I am looking for a quick and easy explanation as to why 0! is 1. Answered by Walter Whiteley and Denis Hanson. 





Why is a circle divided into 360 degrees? 
19960930 

From Kurtis Kredo: I was recently wondering why a circle has been divided in to 360 degrees. When I asked my physics teacher he could not think of an answer. His guess is that it probably has to do with people long ago using the base 6 number system. I have a small inkling that it has to do with easy conversion or usage with radians or grads. Answered by Chris Fisher. 





a to the power zero 
19960603 

From Beti: Why is a number to the power 0 equal to 1? Answered by Harley Weston. 





800 poules pondent 800 oeufs en 8 jours 
20071217 

From LINDA: 800 POULES EN 8 JOURS PONDENT 800 OEUFS, COMBIEN 400 POULES
VONTELLES PONDENT D'OEUFS EN 4 JOURS? Answered by Claude Tardif. 





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. 





exposant 0 
20070125 

From Judith: Je suis stagiaire dans une classe de sixième année et j'aimerais pouvoir expliquer à mes élèves pourquoi tous les nombres exposant 0 donne 1 comme réponse. ( 10 exposant zéro = 1) Merci! 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. 





Exposant à la 0 
20000704 

From Sylvie: J'aimerais savoir combien fait 0 exposant 0. Answered by Claude Tardif. 

