







The angle of a countersunk screw 
20200119 

From Barbie: I need to be able to verify the angle used for the head of a countersunk screw.
I have the diameter of the head, diameter of the shank and height between the
two. I assume it would be considered a frustum.
For example:
A standard 90 degree metric flat head screw in an M2 diameter has a head diameter of 3.65mm,
the actual thread diameter is 1.98mm and the height of the head is 1.20mm.
How can I prove that it is a 90 degree angle? Answered by Harley Weston. 





Macy's coin collection 
20190130 

From Sariah: Macy's coin collection has 2 pennies for every nickel. If she has 60 coins that are pennies or nickels, how many nickels does she have? Answered by Penny Nom. 





Sale price and employee discount 
20190118 

From Margaret: What is the formula to find the
75% off full price item that was already marked 30% off? Answered by Penny Nom. 





Price before VAT and a discount 
20181115 

From Carol: I bought a computer for £330.
The selling price included VAT at 20%.
Then I was allowed a staff discount of £30.
What was it’s original price before the VAT and staff discount? Answered by Penny Nom. 





What is the regular price? 
20170511 

From Saira: If the sale price is 55.50$ and the discount is 12% what is the regular price Answered by Penny Nom. 





How do I establish the original List Price? 
20170115 

From Bob: (1) I have a net price item at $4,664.66 but do not have the discount percentage. I have been told I received 40%? How do I establish the original List Price and to confirm what discount I received? Answered by Penny Nom. 





A 15% discount 
20160809 

From eunice: brian brought a printer sale at the store. the discount was 15%, and brian saved 550. what was the printer original price? Answered by Penny Nom. 





Countable and uncountable sets? 
20160115 

From wilson: what are the countable and uncountable sets? Answered by Penny Nom. 





Three discounts 
20160110 

From Tiffany: Khairul wants to buy a sofa set. He is offered 3 successsive discounts of 10%,20% and 25%, and he can arrange them in any order he wants. Which order will benefit him the most? Explain your answer. Answered by Penny Nom. 





Strings of characters 
20151228 

From Ali: If I have an app and offer a two, three and four digits name and it can be only number, letters or both?
I want to know how many options will I have for each?
For example
the two digits: aa, 11, a1 or 1a
the three digits: 111, a2a, 222
the four digits: 1111, 2ge3 or 1234
So if I used all the letters and all the numbers but nothing starts with a zero
How can I calculate them separately? Or what's the result for each?
Thank you
Ali Answered by Penny Nom. 





Constructing a cross country district schedule 
20151213 

From David: Retired math teacher trying to help soninlaw schedule a cross country district schedule. The would like to have four trimeets each week for five weeks and one week of dual meets. The score the trimeets as three duals, i.e. 1v2, 2v3, 1v3 constitutes one trimeet. After many hours, not sure its possible, but I have forgotten a great deal! Thanks Answered by Victoria West. 





The original price before a discount and taxes 
20151209 

From Michelle: Good day,
I would like to know if there is a particular equation to validate the following information:
I had to find the original cost of an item sold for 759.36$ before a 25% discount and 13% taxes.
I know we must use separate question to obtain the answer but I am unsure how to write the equation to validate my answer. Answered by Penny Nom. 





Discount 
20141220 

From nirmala: A bag is marked at rs 800 and is sold for rs 68. Find the rate of discount Answered by Penny Nom. 





Base 6 
20140910 

From Amanda: using base 6, what is the next number after 25? 35? 55? and 455?
I need to be able to show the base 6 material. Answered by Penny Nom. 





Buying shoes on sale 
20140630 

From Willa: So, I have this question from my summer packet: "Gwen buys 3 identical pairs of shoes at store a. She pays $110.25 after the discount what is the regular price of each pair? ( 40% off)" 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. 





What is the original price? 
20130425 

From Dylan: shirts on sale for 25% off, the sale price is 12.75. What is the original price? Answered by Penny Nom. 





A markup followed by a discount 
20130323 

From edward: A shopkeeper marks his goods to gain 35%. He allows 10% discount for cash payment. What is his profit percent when he sells the goods for cash? Answered by Penny Nom. 





Markup and discount to get a sale price 
20130302 

From Warren:
If you are an ardent shopper you will be aware of the discount (% decrease) marketing strategy to produce the sale price. I began to wonder just how much markup (% increase) was added initially to an item in order to deliver the discounted sale price.
It was simple to construct a formula to convert one to the other.
For example a 30% (mark down) decrease in price required a 42.86% (mark up) to increase the price initially to Tag price. However when I started apply the formulae to a number of circumstances I noticed some very interesting circumstances associated with this relationship
For example a 99.999999% decrease is numerically equal to a 9,999,999,925% increase (huge ratio difference) while conversely a 0.1% decrease is numerically equal to a 0.10010010% increase (Infinitesimally small ratio difference) so the patterns appears logarithmic not linear.
However what really caught my attention was this pattern
See http://www.ozsmart.com/doc/percentage.htm
My questions is why does the decline in the ratio of increases in required mark up (%) price peak at 50 and 51% precisely and then expand again as the percentage move higher
Any explanation would be appreciated Answered by Harley Weston. 





Possible soccer scores 
20121009 

From Riaan: Good day, I would like to know all the possible scores for a set of 5 soccer matches with no more than 5 total goals being scored in any match.
Bearing in mind that there are three outcomes to every match. Win, Lose or Draw.
Could you please help me with this?
Kind regards
Riaan
South Africa Answered by Penny Nom. 





Profit and discount 
20120924 

From ally: A wholesaler purchased a wheat for $150 per tonne.He sold it at $170 per tonne.Calculate the percentage profit to (1 decimal place)if the wholesaler offered a 12% discount on the selling price.What could be the new selling price? Answered by Penny Nom. 





What is the 6001st digit that Sam wrote? 
20110215 

From Sarah: Sam wrote the natural numbers from 1 to 5280 in order. What is the 6001st digit that Sam wrote? Answered by Penny Nom. 





Counting by sevens 
20100413 

From Larry: Lee counted by 7's beginning with one of the whole numbers from 1 through 7, until Lee passed 1000. If Lee counted
three of the following numbers, which number did Lee NOT count?
a. 107
b. 184
c. 534
d. 641
Answered by Robert Dawson and Penny Nom. 





A 25% discount 
20100329 

From Susan: If something costs 1.00/per lb. and that price includes a 25% discount. How do you calculate what the price was before the discount? 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. 





A markup and a discount 
20091115 

From joe: I have a product that cost $ 300.00 I want a 25% markup and give a 15% discount
but keep 25% markup.
300 + 25% = 375
300 + 40% = 420
420  15% = 357
what am i doing wrong???? Answered by Harley Weston. 





Find the original price 
20091106 

From Cyndy: Find the original price of a pair of shoes if the sale price is $98.00 after a 30% discount. Answered by Penny Nom. 





The cube of a number plus five times the number plus 1 
20091012 

From JP: Find a counterexample to the statement: The cube of a number added to the sum of five times the number and 1 is a prime number.The cube of a number added to the sum of five times the number and 1 is a prime number Answered by Penny Nom. 





Sandra's age 
20090924 

From cindy: Sandra is more than 20 years old and less than 60 years old. You can count by 7's to reach Sandra's age. Next year you will be able to count by 5's to reach Sandra's age. How old is Sandra? Answered by Penny Nom. 





Investing in multiple accounts 
20090626 

From Kenneth: Hello:
If an investor has $1000.00 to invest in multiple accounts, and he
wants a total return of 4%, is there one calculation that can be used
to determine what these amounts could be even though there may be
numerous amounts used as answers for most of the following examples?
For example,
Invest $1000.00 @ 2% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, 4% and 5% for total return of 4%.
etc. Answered by Robert Dawson. 





Jon's bank account 
20090103 

From Abigail: Hi, i have an exam soon (monday =[ )
in my revison book, it shows two peoples bank accounts and then it says
"write a formula to show the balence of Jon's bank account after n weeks of 2003"
this is the table show
Jon's Bank account
Weeks 
Week 1 
Week 2 
Week 3 
Week 4 
Week 5 
Balance(£) 
970 
1035 
1100 
1165 
1230 
Answered by Penny Nom. 





Why is the difference between british and american counting? 
20081215 

From Muhammad: Why is the difference between british and american counting?
Example 1 Billion american = 1,000,000,000 but,
1 Billion British = 1,000,000,000,000 Answered by Robert Dawson and Harley Weston. 





A double discount 
20081006 

From Joanna: An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost? Answered by Penny Nom. 





A price reduction and a discount 
20080911 

From Rita: A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an earlybird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars,
x > 100, at 8 a.m., what, in terms of x, is the cost of Hakeem's purchase?
(1) 0.20x  15 (3) 0.85x  20
(2) 0.20x 3 (4) 0.80x  12 Answered by Penny Nom. 





A discount as a percentage 
20080905 

From joeann: if a product sold for $40.00 and you got a $10.00 discount what percentage discount do you recieve? Answered by Penny Nom. 





Aboriginal number groupings 
20080904 

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





What is the account value after 3 years? 
20080710 

From Carlos: Question
Suppose that you deposited $3,000 at the beginning of each year for three years in a savings account earning 4%. What is the account value after 3 years (approx)?
a. 9,120
b. 9,211
c. 9,739
d. 9,989 Answered by Penny Nom. 





A 15% discount 
20080618 

From karonn: Muthu bought the following items from a furniture shop which offers trade discounts of 15% on its furniture.
Item 
list price 
office chair 
RM 250 
office table 
RM 1400 
book shelf 
RM 3500 
(a) find the net price of each item.
(b) find the total payment if Muthu bought 3 office chairs, 2 office tables and a book shelf. Answered by Penny Nom. 





Price discounts 
20080614 

From karonn: Kinky Trading sells an items for RM90 less 25% and 10%. Softee Trading sells the same item for RM100 less 30%.
(a) find the net price of the item for the two companies.
(b) what additional discount percent must be offered by the company that sells at higher net price in order to meet the competitor's price? Answered by Penny Nom. 





The volume of a countertop 
20080308 

From Matthew: I need to calculate volume down to cubic feet. I pour concrete countertops
and cant figure out the formula to convert inches and feet. If I have a 2.5 inch
by 2 foot by 16 foot concrete countertop how do I convert it to cubic feet
and hence know how many bags of concrete at .6 cubic feet per bag I will need.
I am trying to input the formula into a spreadsheet. thank you so much Matt Answered by Penny Nom. 





Cantor's diagonal argument 
20080126 

From David: Cantor's theory using a diagonal across a list of real numbers to proven uncoutability has always puzzled me.First in base ten, it feels like hocus pocus so I began thinking of the Boolean numbers as truer representations of place value (on,off). Secondly his list was always arbitrary or so I recollect. Therefore, I suggested using a seriesA=.10000....,B=.01000. C=.11000, etc.
Any diagonal is already located among the numbers listed. My only alteration is that since the final digit is always unrepresentably either one or zero, but it must be one or the other, I make an assumption that if x= .abc...1 and y= .abc...2 the only two possibilities and I choose to count F=x+y then then the numbers are countable= Z=sumFi,where I=2+2^2+2^3...
I hope this sketch is enough description, I asked Rudy Rucker more formally but got no mathematical response, someone else gave me some tale about slippery epsilon. What do tyou think of recasting his proofs in more rigorous form?
David French Answered by Claude Tardif and Walter Whiteley. 





How many cubes have one face painted red? 
20071127 

From Ashutosh: A rectangular block measuring 10 units by 8 units by 6 units is made up of cubes measuring 1 unit on a side. The base of the block is 10 units by 8 units. The outside of the block other than the base is painted red. How many of the unit cubes have exactly one face painted red? Answered by Stephen La Rocque and Penny Nom. 





A 15% discount 
20071117 

From Deanna: if I purchase an item for $450.00 but get a discount 15% of my item what would then be my total Answered by syeve La Rocque and Penny Nom. 





A 10% markup then a 10% discount 
20071113 

From svetik: The best selling dessert at Chez Russell earns revenue of $5000 per week. During Restaurant Week, they are required to give a 10% discount on this dessert. Because the owner is a crook, he decides to mark up the price the week before Restaurant Week and then give the 10% discount off the marked up price. During the marked up week, they still sold the same amount of pieces as any prior week. However, they expect to sell 100 more pieces during restaurant week. If the revenue from this dessert is the same for the marked up week and restaurant week, what is the normal price of the dessert, rounded to the nearest cent? Answered by Penny Nom. 





How students learn math in other countries 
20070920 

From Patricia: I'm desperately searching the web for information on how students learn math in other countries. Years ago I had some worksheets that explained the addition algorithm as it was taught in other countries. That is the sort of thing I need. I teach 6th grade math in an urban school and have many students from other countries (Mongolia, Somalia, Ivory Coast, Honduras, Serbia) I want to celebrate their heritage while helping them learn the basics of 6th grade math. Answered by Diane Hanson. 





Segments on a line 
20070910 

From Cathy: This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments. Answered by Penny Nom. 





Four digit numbers with at least one three 
20070815 

From Alberto: How many fourdigit numbers are there which contain at least one digit 3? Answered by Stephen La Rocque. 





More on the cardinality of sets 
20070727 

From Mac: Can you please help me to find and verify whether the following are
finite, countably infinite and uncountable ? Answered by Harley Weston. 





Countable and uncountable sets 
20070724 

From Mac: Hi, i tried to read few webpages related to the countably infinite and uncountable sets.
Even i read few questions from this forum.
But i am not convinced with this explanation. If you have any good book that
explains this in layman term, please redirect me to that.
1) Can you please explain what is the difference between these too ?
2) How could you say set of Natural number and set of even numbers are countably
infinite ?
N={1,2,3,...} and Even= {2,4,6,...}
When an element in the even set is some 2n, we will map it to 'n'.So
now we have a bigger number(2n) right ?
Sorry, i didn't understand that.
...
Can you please help me out to understand that ? Answered by Harley Weston. 





How many diagonals does a polygon have? 
20070718 

From Edna: how do you find the numbers of diagonals of a polygons? Answered by Stephen La Rocque. 





Discount percentage 
20070711 

From Greg: List Price: $50.00
Discount: 33 1/3%
What would the net price be? Answered by Stephen La Rocque. 





Counting squares 
20070512 

From Bridget: Explain how many squares there are on a board measuring 4 by 4 units, Answered by Stephen La Rocque and Penny Nom. 





Choosing a bicycle 
20070328 

From Jackie: A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible. c) List the sample space. Answered by Penny Nom. 





Seven digit account numbers 
20070309 

From Miranda: Account numbers for the Central Oil Company consist of seven digits. If the first digit cannot be 0, how many account numbers are possible? Thank you so much!!! Answered by Penny Nom. 





A counterfeit coin 
20070305 

From Delian: Hi there, I have a counterfeit penny problem  however this one is slightly more challenging. I have twelve pennies, and one of them is counterfeit. The only difference between the counterfeit coin and the real ones is that the counterfeit is EITHER heavier or lighter than the others (We don't know which). I need to be able to solve this in only three weightings, and I REALLY NEED HELP!!! Answered by Penny Nom. 





Weightng coins 
20070218 

From Gary: You are considering buying 27 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin. Answered by Penny Nom. 





Countable and uncountable sets 
20070213 

From piyush: we se that union of countably infinite no of sets having countably infinite number of elements is a countable set we can express p(n) (i.e power set of natural number) as a union of countable infinite number of sets i.e p(n)=s1Us2Us3..... where s1=null s2={1,2,3,4,5..........} s3={{1,1},{1,2},{1,3},..............{2,1},{2,2}........} using the same statement can we prove that power set of natural number is a infinit countable set Answered by Penny Nom and Claude Tardif. 





Six digit numbers 
20070209 

From marisa: how many six digit numbers can you write using the digits 0 and 1 as many times as possible? Answered by Stephen La Rocque. 





The real numbers with decimal representations consisting of all 1s. 
20061029 

From Ivessa: Determine if the following set is countable or uncountable : the real numbers with decimal representations consisting of all 1s. Answered by Steve La Rocque and Walter Whiteley. 





How many sequences are possible? 
20061028 

From Sam: A fair eightfaced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible? Answered by Penny Nom. 





Math and using fingers 
20061026 

From Portia: Should students be allowed to use their fingers to learn math and why Answered by Walter Whiteley. 





A remainder of 1 
20060913 

From Juan: What is the smallest counting number which when divided by any of the numbers 2,3,4,5,6,,7,8,9 and 10, leaves a remainder of 1? Answered by Paul Betts and Claude Tardif. 





The cartesian product of a countably infinite collection of countably infinite sets 
20060325 

From Geetha: Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite? Answered by Penny Nom. 





Four digit numbers 
20060325 

From Kenvin: i was wondering how many possibilities is there for a four digit number with the same first two numbers and the last two is not one of the first with numbers 19 Answered by Stephen La Rocque. 





Five digit numbers 
20060325 

From Tony: Can someone tell me how many unique five digit numbers can be generated using 09? Answered by Stephen La Rocque and Penny Nom. 





A bill with a 15% tip and a 10% discount 
20060320 

From Tracy: A $4500 bill is presented, without tax. 10% discount coupon. Add 15% tip with 3 people spitting for the sever. Answered by Penny Nom. 





A 35% discount 
20060219 

From Marc: If Julie paid $455.00 for a television and it was already discounted by 35% what was the original price? Answered by Penny Nom. 





Counting digits 
20060130 

From Cynthia: I would like to know the easiest way to calculate the
total numbers of digits used by a printer to number the pages of a book from 1 to 250. Answered by Penny Nom. 





Markups and discounts 
20060121 

From Dan: I'm trying to increase my pricing by 30 percent. I'm doing something completely wrong. If my price is $150.00 and I increase the price by 30 percent. I would take 150 times .30 and that equals 45. I would then take 45 plus 150 and that would give me 195. My problem is now 195 is my list price. If I turn around and give my customer a 30 percent discount off the 195 the price ends up being 136.50. Which is less than the 150 that I started with. I'm confusing myself and have totally lost confidence in what I'm doing and how . Can you help me? Answered by Penny Nom. 





Percentage discount 
20060115 

From Louise: Avril is buying a computer. She finds two places with a discount."Classy Computing" is selling a computer that was £650 and NOW it has £50 off.
"WWW.CHEAPO.COM" is also selling a computer that is £650 but it NOW has 10% off.
WHICH IS CHEAPER? Answered by Penny Nom. 





More on the origin of integers 
20051220 

From A student: have a math extra credit project and we have to go online and look up the origin of integers and I can't find it anywhere do you know?????? Answered by Harley Weston. 





5 digit numbers that include 5 and exclude 8 
20051104 

From Paul: figure out
how many 5 digit numbers are there that include the digit 5 and exclude the
digit 8.
show me how to do get to the answer. (23816) Answered by Paul Betts. 





Divisibility by each of the first ten counting numbers 
20051017 

From Simon: determine smallest positive integer that is divisible by each of the first ten counting numbers Answered by Penny Nom. 





Can one place 15 integers around a circle... 
20050820 

From Hernan: Can one place 15 integers around a circle so that the sum of every 4 consecutive numbers is equal either to 1 or 3? Answered by Claude Tardif. 





The number of four digit combinations 
20050809 

From Kevin: My 12 year old has asked me how to figure out the number of four digit combinations possible using 0 thru 9 without repeating a number? Answered by Penny. 





In how many ways can 12 different fruits be distributed 
20050613 

From Sapta: In how many ways can 12 different fruits be distributed among 3 boys so that each receives at least 1 fruit? Answered by Claude Tardif. 





A six digit answer 
20050518 

From Angela: I have a 6 digit answer that is comprised of only 4 symbols: a square, a circle, a triangle, and an X. How many possible solutions are there and how is the best way to find out what ALL the solutions are? Answered by Penny Nom. 





A countably infinite collection of countably infinite sets 
20050226 

From Feroz: Suppose a set can be divided into a countably infinite number of countably infinite sets.Then can the original set be considered as a countably infinite set? Answered by Penny Nom. 





There are 4 contestants in a bicycle race. 
20050105 

From Robert: There are 4 contestants in a bicycle race. In how many different orders can they cross the finish line? Answered by Penny Nom. 





Six digit numbers with at least one 7 
20041227 

From Behzad: How many sixdigit numbers contain at least one 7 in their decimal expansion? Answered by Penny Nom. 





Visitor wins or home wins 
20040929 

From Paavn and Laddi: I have a math question i am stumped on for one of my classes. The question states that there are 14 baseball games with 2 possible outcomes for each game, visitor win or home win. How many different total combinations are possible from the 14 games? Answered by Penny Nom. 





105.6 is a discount of 12% from x 
20040910 

From David: If I know that 105.6 is a discount of 12% from x, how do I find x?? Answered by Penny Nom. 





Baseball games 
20040314 

From Fabian: Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth.
Answered by Penny Nom. 





Profit, markup and discount 
20040222 

From Kick: Using the calculation on your website, if I sell something for $885 and my cost is $296, I make $589 profit. How do I calculate the profit percent I made on that transaction?
Profit as a percentage of what it cost me?
Profit as a percentage of what I sold it for?
Answered by Penny Nom. 





Pairing boys and girls 
20040201 

From Terri: Suppose 7 boys and 7 girls are assigned to work in pairs of one boy and one girl. Explain what equation can be used and how you would use a simpler problem to solve these types of questions. Answered by Penny Nom. 





A counterfeit coin 
20040123 

From Kim: You are considering buying 45 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin? Answered by Penny Nom. 





Six letter words 
20040117 

From Debora: An anthropologist discovers an isolated tribe whose written alphabet contains only six letters (call the letters A, B, C, D, E, and F). The tribe has a taboo against using the same letter twice in the same word. It's never done. If each different sequence of letters constitutes a different work in the language, what is the maximum number of six letter words that the language can employ? Answered by Penny Nom. 





Chisenbop 
20031106 

From Jaclyn: Hi there i was wondering if you would have any information on "counting on your fingers" or " Chisabop". Answered by Penny Nom. 





nine digit numbers 
20030723 

From John: With a nine digit number, with each of the nine digits having a possibility of 10 different numbers then what is the total number of possible mathematical variations in the nine digit number. i.e. Social Security numbers have nine digits and if each of the nine digits have a possibility of being any one of ten numbers, i.e. 0,1,2,3,4,5,6,7,8,9. Then what is the formula to calculate the maximum possible number of variations in this nine digit number and what is the mathematical maximum possible number of variations of this nine digit number? Answered by Penny Nom. 





Mary typed a six digit number 
20030306 

From Pillar: Mary typed a six digit number, but the two 1's did not show. What appeared instead was 2002. How many different sixdigit numbers could she have typed? Answered by Penny Nom. 





The number of possible outcomes with 8 games 
20030221 

From Gianni: If 8 basketball games being played(no ties), which means a total of 16 teams, what are the total number of possible outcomes that can occur. Answered by Penny Nom. 





6 digit numbers from 0,0,2,2,4,4 
20030123 

From Amanda: How many 6 digit numbers can you make from the numbers 0,0,2,2,4,4, giving that 0 cannot come first. The number has to contain 2 twos, 2 fours, and 2 zeros. Answered by Penny Nom and Claude Tardif. 





A penny, a nickel, a dime, a quarter, and a loonie 
20030121 

From Blaine: I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? Answered by Penny Nom. 





Combinations of 1,2,3,...,10 
20021127 

From Gord: If I had the numbers from 110 how many different combinations would i have.....would it be 100....since that is 10 squared. Answered by Penny Nom. 





The horse race 
20021119 

From Pat: The Horse Race Three horses run a race. In how many different ways can the three horses finish the race if ties are allowed? Answered by Penny Nom. 





Chisanbop 
20021107 

From Paul: I'm trying to find the book/books that explain this system? I have one small book that explains the very beginning of the system, but covers only about 10 to 20%. I'v tried several book sellers and have had no luck. Answered by Diane Hanson. 





How many empty seats are there? 
20021029 

From Ronnie: Three new students arrived in class. Teacher says there are 210 ways you can set. How many empty seats are there in the classroom? After new student are assigned seats, how many empty seats will remain? Answered by Penny Nom. 





Tree diagrams 
20021012 

From Denean:
 For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?
 In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?
Answered by Penny Nom. 





How many dominoes? 
20020913 

From A student: Dominoes are split into two halves. If you were allowed up to 6 dots on each half, how many options of dominoes could you get? Answered by Penny Nom. 





Social security numbers 
20020906 

From Chris: How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 09 in multiple different spots. Answered by Penny Nom. 





Parallelograms 
20020821 

From Moorthy: 11 parallel lines are intersected by another 9 parallel lines.Then how many parallelograms are formed? Answered by Walter Whiteley. 





Combination locks 
20020817 

From John: How many combinations of three number codes can occur with a standard combination lock? The range of possible numbers is 039 which allows 40 different possible choices each turn of the dial. Each combination requires exactly three numbers (i.e. three turns of the dial). E.g. 35405. Allow for reuse of the same number three times e.g.101010. I don't think there is any preference shown for certain number combinations. Can you explain how the total is derived? Someone at the YMCA this week put this question to me and I gave an answer but I am not sure I am rightso I have come to you. Answered by Penny Nom. 





Musical Scales 
20020724 

From Terence: Given that there are 12 notes in a musical octave, what is the maximum number of musical scales possible within that octave, if each scale has a minimum of 5 notes and a maximum of 9 and we start all the scales from the same note? In case you don't know anything about music, a scale is a progression of notes where you start on a specific note and end on that same note an octave higher. There are twelve different notes between these two similar notes. Which notes you choose to play determine the sound of the scale. Anything less than five notes would not make for a very interesting scale. Anything more than nine and you would be playing almost 'every' note in the scale, not leaving much room for distinction in how you organize these notes. I assume you first have to figure out the maximum number of variations possible in a 5note scale (with 12 notes at your disposal). Then do the same for a 6note scale, then a 7note, then an 8note, and so on. Then add up the results. How to find this maximum number of variations for each scale size though is what I don't know. Answered by Leeanne Boehm. 





Counting 
20020621 

From Rachel: How many different numbers of 2 different digits each can be formed using the digits (1,3,5,7,9)?
How many triangles are formed by the vertical of a regular hexagon? Answered by Penny Nom. 





The cross country team 
20020612 

From Denae: In cross country, a team's score is the sum of the first five finishers on the team. The captain of the team finished 2nd in the meet. The next four finishers on the team placed in consecutive order. The team score was 40. in what places did the other members finish? Answered by Penny Nom. 





A popular television game show 
20020519 

From Amrita: On a popular television game show, contestant must first answer a question by placing 4 given events in ascending or desending order in the quickest time. (a) if a contestant does not know how any of the events should be arranged, how many different ways could the question be answered?
Answer: 4!= 24 (b)a contestant has to arrange the events that correspond to A, B, C, and D. one contestant is positive that event D follows directly after avent B, but does not know about the other s. how many different ways could this contestant arrange the letters A, B, C, and D, list the possibility
Answer: which I didn't get Answered by Penny Nom. 





A ski trip 
20020510 

From Navi: A ski trip at the school has been arranged. there are 30 students that have paid for the trip and 6 parents that have volunteered to chaperone. to transport the students and parents easily, they are to be divided into two group. one group has 10 students and 2 parents, and the other group has 20 students and 4 parents. (a) How many different group of 10 students can be formed? ANSWER:
(b) How many different groups consistinmg of 10 students and 2 parents are possible? ANSWER:
(c) kelly is one of the students going on the ski trip, and kelly's mother volunteered to be one of the chaperones. kelly's mother would prefer to be in the smaller group and not in the same group as kelly. if this wish is honoured, how many ways can the smaller group and its chaperones be chosen? ANSWER: Answered by Harley Weston. 





Designing a ballot 
20020426 

From Kelley: I want to design a ballot for four elections. Actually all the candidate races are on 1 ballot. I need to know how many different ballot styles would be needed for all of the candidates to be in each rotation an equal number of times. For example:  A,B,C & D are running for mayor
 E,F,G & H are running for congress
 I,J & K are running for senate
 L,M & N are running for governor
They are all on the same ballot. But in each race their name (for instance A) has to be in the #1 rotation, #2 rotation, #3 rotation, and #4 rotation for his race on this ballot an equal number of times as B,C and D. The same goes for the other candidates for their perspective races. How many total ballot styles will there be? Answered by Penny Nom. 





How many different account numbers are possible? 
20020418 

From Andrene: how many different account numbers are possible if the account numbers consist of a letter of the alphabet, followed by five numerical digits, and followed by another letter. 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. 





A health club 
20011125 

From Maria: A health club with a membership of 650 people operates a running track and an indoor swimming pool. A survey of the membership indicates that 68% use the running track, 44% use the swimming pool, and 8% use neither. If a member is chosen at random, what is the prbability that the member uses: a) Both the track and the pool? b) Only the track? Answered by Penny Nom. 





Cardinality of sets 
20011119 

From Tania:
 Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}.
 Show that (the cardinality of the natural numbers set) N = NxNxN.
 Show that the cardinality of the set of prime numbers is the same as the cardinality of N+
Answered by Walter Whiteley. 





Subsets of a countably infinite set 
20011114 

From Tania: How could I show (and explain to my son) that any countably infinite set has uncontably many infinite subsets of which any two have only a finite number of elements in common? Answered by Claude Tardif. 





Counting CD's 
20011106 

From Jason: An older brother said to his younger brother, "Give me 8 of your CDs, then I will have twice as many as you." The younger brother replied, "No, you give me 8 of yours instead, and then we'll have an equal number." How many CDs does each boy have? Answered by Chris Fisher. 





Free pamphlets 
20011024 

From Salman: a travel agency has limited number of six different free pamphlets about the beetle islands. the agent tells you to take any that you want, but not more than two of any kind. Assuming that you take at least one pamphlet, how many choices could you make Answered by Penny Nom. 





Counterclockwise 
20010914 

From Rolanda: When Descartes invented the coordinate system he decided to number them counterclockwise. Why? Answered by Chris Fisher. 





Buying a car 
20010606 

From Steph: How do you figure a percent. Say you want to buy a car listed for 21,500. You tell the dealer you want to pay 19,600. The dealer says they'll sell it to you for 20,450. how do you figure what the percent is between 20,450 & 19,600? Answered by Penny Nom. 





Danging couples 
20010606 

From Danielle: How many boygirl dancing couples could be formed if 85 boys and 102 girls attend a school dance? Answered by Penny Nom. 





Four digit numbers from 1,2,3,4,5,6,7,8 
20010531 

From Katie: Okay.......here's my question...how many different ways can you form a four digit number out of these digits..1,2,3,4,5,6,7,8? This is how my teacher said to do this.... 8*8, 7*7,6*6,5*5,4*4,3*3,2*2,1*1. then she said to add up the products and to multiply by 7. is this correct, and if not how can you figure this out. Answered by Penny Nom and Claude Tardif. 





A 6 character field 
20010516 

From A parent: I have a 6 character field that can use any combination of alphanumeric characters (AZ, 09). How many total combinations are possible? Answered by Penny Nom. 





Dominos 
20010428 

From Mark: A standard dominoe set consists of 28 pieces, from doublezero to doublesix  Is it possible to arrange all those pieces in a straight line in such a way that the dots of any pair of adjacent pieces match? Please include picture
 Is it possible to arrange them in a circle and still meet the conditions in 1?
Answered by Claude Tardif. 





Choosing a car 
20010428 

From Ashley: THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE? Answered by Penny Nom and Andrei Volodin. 





Four crayons 
20010110 

From Neyra Espinoza: You have four crayons (red, blue, yellow, green). If you line them up, how many different combinations can you get? Answered by Patrick Maidorn. 





5 spades 
20001121 

From Matt: In a standard deck of 52 card how many would you have to draw (without looking at them) to be absolutely certain that you had 5 spades? Answered by Claude Tardif. 





Permutations vs. combinations 
20001120 

From Ashleigh: How do you tell whether the problem is a permutation or a combination? Answered by Walter Whiteley. 





Two problems 
20001102 

From Michael: Question: I mistakenly divided a number by 5 when I should have multiplied by 5. FInd my percent of error. Next Question: How many odd numbers are between 10 and 9,999 from the digits 09 if each digit is used once per number. Answered by Penny Nom. 





Tapes and CD's 
20001022 

From Arnold: Nicole has 25 CDs and tapes altogether. When she tries to pair them up, she has 4 CDs left over. How many tapes does Nicole have? Answered by Penny Nom. 





Probability of a square 
20000918 

From Nick: What is the probability that four different points chosen at random from the fifteen equallyspaced points shown are the vertices of a square? I need to have my answer expressed as a common fraction. Help! I don't know how to write it. . . . . . . . . . . . . . . . Answered by Penny Nom. 





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. 





Six letter words 
20000515 

From Karl Freitag: An anthroplogist discovers an isolated tribe whose written alphabet contains only six letters (call the letters A,B,C,D,E, and F). The tribe has a taboo against using the same letter twice in the same word. It is never done. If each different sequence of letters constitutes a different word in the language, what is the maximum number of sixletter words that the language can employ? Answered by Penny Nom. 





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. 





Question regarding Combinations and permutations 
20000419 

From Paul Stoner: I am a programmer and I have a quick question. I have 5 criteria which will either be true or false. If a criterion is true it returns its ordinal representation, if false it returns 0. I then combine these results to determine where to go in my program. My question is: How can I figure out the number of combinations I will need? Answered by Patrick Maidorn. 





Hats, jackets and gloves 
20000330 

From Max: Find the one that does not belong 66 333 99 111 88 also if you have 3 hats and 3 jackets and 3 gloves, how many different combinations of a hat and a jacket and gloves can you wear? Answered by Claude Tardif and Penny Nom. 





Six digit numbers using 1,2,5,6,7, and 9 
20000320 

From Rachel: How many different sixdigit numbers can you make using the digits 1,2,5,6,7, and 9? How many of these six digit numbers are divisible by six? Answered by Claude Tardif and Denis Hanson. 





Party favors 
20000222 

From Krystina Fernandez: Luanne was making party favors for her little sister's birthday party. Each party favor was in the shape of a cube. Luanne had pink and purple paint to paint the cubes and she could paint each face only solid pink or solid purple (no dots,stripes,ect.).For example, one cube may be all purple, another may have two purple faces and four pink faces. Her little sister wanted to have a different cube for each guest.(A cube is not considered different if it can be turned so that all it's sides match the corresponding sides of another cube.)How many different cubes was it possible for Luanne to make? Answered by Claude Tardif. 





Why counterclockwise? 
20000221 

From Drew: Why do the numbers of quadrants in a graph increase in a counter clockwise pattern? Why aren't they numbered increasingly in a clockwise pattern? Answered by Chris Fisher. 





Change for a dollar 
20000216 

From Rachelle: What is the least positive number of coins that is impossible to give out change for a dollar? It is higher than 50 i know and you can us dimes, nickels, pennies, quarters, 50 cent pieaces and silver dollars. Answered by Claude Tardif. 





Ten stools 
20000206 

From Haim: In a cafe with ten stools, three customers want to be seated, so that no two are next to each other. How many ways can this be done? Do not consider it to be a separate seating if two customers switch seats. Answered by Denis Hanson and Walter Whiteley. 





Phone Number Possibilities 
20000109 

From Hamilton Weston: How do phone companies arrive at the possible number of phone numbers that can be generated for customers? Answered by Harley Weston. 





The number of city blocks in a country mile 
19991124 

From Gloria Hearst: For years my family has had an on going debate on the number of city blocks in a country mile. We vary from a minmum 8 blocks per mile to a maximum of 12 blocks per mile. Answered by Nadine Griffiths and Penny Nom. 





Clockwise or Counterclockwise? 
19991027 

From Tim: A particle moves around the circle x^{2} + y^{2} = 1 with an xvelocity component dx/dt = y  Find dy/dt
 Does the particle travel clockwise or counterclockwise around the circle? Why?
Answered by Harley Weston. 





Going to the movies 
19991021 

From Gayla Werry: You have $1.00 to take 100 people to the movies. It costs: 1 cent for 10 children, 3 cents for each woman, 5 cents for each man. You have to take at least one of each category of people. Your answer has to add up to exactly 100 people and exactly $1.00. How many men, women, and children can you take? Answered by Penny Nom. 





How many squares are on a chessboard? 
19991020 

From Tchilco: How many squares are on a chessboard? Answered by Penny Nom and Claude Tardif. 





towers of cubes 
19991005 

From Sanker: I need help to solve this Rules for bulding towers of cubes rule 1  The number of cubes on the bottom layer is always one less than the number of squares on the grid  rule 2  Each new layer is made with one cube less than the layer underneath it.   Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid
 investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid
 investigate the relation between the number of arrangements of cubes and the size of the grid
 when there are two layers of cubes
 when there are more than two layers of cubes
Answered by Walter Whiteley. 





Numbers with the digit 2 in 1...1000 
19990920 

From Jessica: Is there a trick to finding out how many numbers containing the digit two is there from 1 to 1000? Answered by Walter Whiteley. 





The birthday problem 
19990419 

From Gordon Cooke: How do I explain the rapid rise in the probability that at least two people in a group of n have the same birthday. We have derived the formula for p(n) and have graphed it and have seen how the results are counterintuitive. At around n=23 p(n)=.5 and at n=50 p(n) is very close to 1. It does not help to simplify the problem (eg use months instead of days) because then our intuition does correspond more closely to reality. Is there some way we can see how the probabiltiy of a "collision" increases with n? It makes me think of data storage problems and hash tables in computer science. Answered by Harley Weston. 





Dividing a Circle 
19990412 

From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example  1 line divides the circle into 2.
 2 into 4.
 3, however into 7.
 4 into11
 5 into 16
 6 into 22
 7 into 29
 8 into 37
 etc...
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom. 





Four Corners Maths Problem 
19990216 

From Helen Williams: I am currently a student teacher in the UK and I have to write a 1000 word report on the following maths problem which I am completely stuck on! PLease HELP!! Choose and 3 by 3 section of the hundred square. Add the total of the four corners. How many different groups of four numbers can you find that add up to that number? eg, Total of 4 corners add up to 48. Adding 2, 13, 22, 11 also make 48 etc.. How many different groups of 4 numbers would add up to 48? How would these results compare with thoses obtained from a 3 by 3 square in which the numbers are consective? eg, PLEASE HELP AS I AM COMPLETELY STUCK? WHY DO ALL THESE DIFFERENT WAYS ADD UP TO THE SAME NUMBER?? Answered by Harley Weston. 





Grade 4 curriculum 
19990209 

From John: My daughter is in grade 4 and her math teacher has asked her to write out the number 1 to 10,000. She is currently at 4567 and is sick of it. When I complained that this was not a usefull exercise she said that the Ministry of Education curriculum requires this and gave a photocopy of the page. It states: "read and write whole number to 10,000 in standard, expanded, and written forms (eg., 9367=9000+300+60+7 = nine thousand three hundred sixtyseven). Has the teacher interpreted this the wrong way? Thanks John PS. Do you have a web address for Ontario Math and Science Teachers organization? Answered by Jack LeSage. 





Money and Counting 
19990203 

From Deborah Goodman: I am looking for ways to tutor my daughter in money counting and handwriting skills. Answered by Jack LeSage. 





A handshake problem 
19990105 

From Nick Lam: There are 40 people at a party. 1 host couple, a mom and her daughter. There are 19 other guest couples, composed of moms and their daughters. The Host couple shakes hands with everyone except each other. Each guest mom shakes hands with everyone but their own daughter. Each guest daughter shakes hands with everyone except their own mom. A hand shake between two people is considered to be one handshake. HOW MANY HANDSHAKES ARE THERE? Answered by Penny Nom. 





Three dice 
19981117 

From Ryan Allinson: Rolling three regular dice how many different ways could a sum of 10 be rolled? Hope you can help. Can you please show me how this is done? Answered by Penny Nom. 





Percentages 
19980710 

From Adam: Hi, I would like to know the basics of percentages. It is all rather confusing to me.I have excelled in math but want to be ready next year for more advanced math. What is Percentages? Answered by Penny Nom. 





Social Security Numbers 
19980707 

From Valerie Lucas: How many social security numbers are possible? the answer is 10^9 why isn't the answer 9^9? Answered by Harley Weston. 





The Birthday Problem 
19980612 

From Josh Skolnick: if you are at a party what is the least amount of people that have to be there to have at least a 50% chance of having 2 people with the same birthday? and how do you get the answer thank you in advance josh Answered by Harley Weston. 





Using your fingers 
19980421 

From Ian Sutherland: My 7yearold son, in Grade 2, constantly uses his fingers to count. I know for now this is a useful crutch but at what point should he stop? Answered by Diane Hanson. 





A Finite Math Question. 
19970907 

From Angela L.: How many threedigit numbers can be formed using only the numbers 1 to 7 if the number 2 must be included? Answered by Penny Nom. 





Circular Permutations 
19970205 

From Ed Varjassy: I have an understanding of simple problems involving circular permutations but do not understand them when they start to have restrictions. Is there any advice you can give for these more complicated permutations. Answered by Penny Nom. 





Diagonals in a polygon 
19960618 

From Steven: How many diagonals are there in a polygon? Answered by Denis Hanson. 

