







Three consecutive odd integers 
20200410 

From Roxie: What is three consecutive odd integers? Answered by Penny Nom. 





Odds 
20191216 

From Craig: I’d like to know what are the odds of a lotto machine giving out a specific 4 digit number as a quick pick?
I know there are 10,000 possible 4 digit combinations. So let’s say the number is 3587 what are the odds the lotto machine spits it out EXACTLY that way on a quick pick? Answered by Penny Nom. 





Four odd factors 
20180704 

From Manchali: Find a number that has 4 factors and all of them are odd numbers. Answered by Penny Nom. 





Two odd integers 
20180604 

From Pleroma: The product of two alternate odd integers exceeds three times the smaller number by 12.
What is the larger number? Answered by Penny Nom. 





Three consecutive odd integers 
20171010 

From Johanna: Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third Answered by Penny Nom. 





Two consecutive odd integers 
20170714 

From Adeeb: Find two consecutive odd positive integers, sum of whose square is 290. Answered by Penny Nom. 





Divisibility of 3n^5+7n 
20161214 

From Parag:
Question from Parag, a student:
if n is a natural number,then 3n^5+7n is divisible by
a)2
b)3
c)5
d)7
i got the answer but still i need a valid alternate approach. Answered by Penny Nom. 





The sum of three integers is 30 
20161206 

From Vaishnavi: _+_+_:30. Blanks are to be filled by(1,3,5,7,9,11,13,15) and numbers can be repeated. 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. 





A 13 game bet 
20160228 

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





Two consecutive odd integers 
20150309 

From gowtham: The sum of two consecutive odd integers is 20.find the integers Answered by Penny Nom. 





Even and odd 
20141128 

From Subrahmanya: n1, n2, n3....................,n1997 are integers not necessarily distinct. (actually in n1, n2,.............., n1997 the numbers 1,2,.................,1997 are subscripts of 'n')
X= (1)^n1+(1)^n2+............+(1)^n998
Y=(1)^n999+(1)^n1000+............+(1)^n1997
Then
which of the following options is true
A) (1)^X = 1, (1)^Y = 1 B) (1)^X = 1, (1)^Y = 1
C) (1)^X = 1, (1)^Y = 1 D) (1)^X = 1, (1)^Y = 1
E) none of these Answered by Penny Nom. 





Three consecutive odd integers 
20141017 

From Maddy: 3 times the largest of three consecutive odd integers is 13 more than the sum of the other two. What are the integers? Answered by Penny Nom. 





The largest odd number using the digits 08672 
20140624 

From audrey: what is a 5 digit greatest odd number out of this given digits? 08672 Answered by Robert Dawson. 





Consecutive Numbers Question 
20130811 

From Lucy: Hello,
I have a question about consecutive numbers. So lets say a question tells you to find what three consecutive numbers are that add up to a certain number. To calculate this, would you use
2x+1, 2x+3, 2x+5 or just x, x+2, x+4.
Also, the same question for even numbers. Would you use:
2x, 2x+2, 2x+4 or just x, x+2, x+4.
My math book is confusing because it uses the first strategy(the 2x+…) in some situations and the second strategy(x+…) in other situations. Thus, can you provide me an explanation of why you would use the strategy that is correct?
Specifically, my book answered this question: If “n” is the first of five consecutive odd numbers, what is their average, using n,n+2….=5n+20 and average is n+4(this is the answer),.
For the question: the sum of 4 consecutive odd integers must be:
Divisible by 8 but not necessarily 16(this is the answer), it used the strategy 2k+1, 2k+3…=8k+16.
Thank you so much for taking the time to answer my question. Answered by Harley Weston. 





Three consecutive odd integers 
20130708 

From sparsh: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: Answered by Robert Dawson. 





If n is odd, then n^2  3 is even 
20121211 

From Tracy: Prove the statement:
For all integers n, if n is odd, then n2  3 is even. Answered by Penny Nom. 





The square of any odd number, decreased by 1, is divisible by 8 
20121116 

From bailey: Prove that the square of any odd number, decreased by 1, is divisible by 8 Answered by Penny Nom. 





4 digit combinations 
20121017 

From Scott: How many different 4 number combinations from 0123456789 with 2 out of the 4 odd and 2 out of the 4 even, with no numbers repeating. Thanks Answered by p. 





15 pigs and 6 pens 
20111116 

From Mike: I have 15 pigs and 6 pens, I have to put them in odd numbers, how do I do it. Answered by Chris Fisher. 





Twice an even number 
20111010 

From Ron: The number of dollars that Tracy has in her pocket is an odd number.
Hal gave Tracy $2 more than she already had in her pocket.
The number of dollars Tracy now has cannot be _________.
a) $60 b) $62 c) $64 d) 68 Answered by Penny Nom. 





Three consecutive odd integers 
20111007 

From Muneera: Find 3 consecutive odd integers so that 3 times their sum is 5 more than 8 times the middle one? Answered by Penny Nom. 





A four digit number 
20110916 

From gina: i am having a hard time figuring this out.. i believe the answer is 3105 but the 0 is throwing me off... i am a 4 digit number between 3100 and 3200, none of my digits are even, the sum of my digits is 9, the largest digit is in the ones place, what number am i ?? Answered by Penny Nom. 





Three consecutive odd numbers 
20110311 

From George: Write an equation three consecutive odd numbers whose sum is 75 Answered by Penny Nom. 





Three consecutive odd integers 
20101107 

From karen: find three consecutive odd integers such that twice the sum of the second and the third is 43 more that three times the first Answered by Penny Nom. 





Can a fraction be an even or odd number? 
20100825 

From Kenneth: Can a fraction be an even or odd number? If not , why? Answered by Stephen La Rocque and Harley Weston. 





A collection of baseball cards 
20100701 

From Martha: Cody has a collection of baseball cards. Is it possible for him to
place the cards into 5 boxes so that exactly 3 of the boxes contain an
odd number of cards and the total number of cards in two of the boxes
is the same as the total number in the other 3 boxes? Explain. Answered by Robert Dawson, Penny Nom and Claude Tardif. 





Odd integers 
20100528 

From jack: If x is an odd integer, which of the following must also be an odd integers
a) x+1; b) 2x; c) x+4; d) x1; e) x/2? Please help me to solve this problem. Thank you. Answered by Penny Nom. 





Odd numbers with no repeated digits 
20100501 

From jameka: How many odd numbers can be written from the set {2,3,4,5,6} if no digits may be used more than once? Answered by Penny Nom. 





7 odd numbers 
20100219 

From mike: Hello there,
Problem: find 7 odd numbers who sum is equal to 30.
Hint*My professor said it's possible to add 7 odd numbers and get 30 for an answer!
and he said we can use Negative and rational numbers but no decimal or fractions.
So is there anyway of solving this? Please get back to ASAP! thanks. Answered by Harley Weston and Tyler Wood. 





Three digit odd numbers 
20100204 

From Rebecca: Question from rebecca, a student:
how many three digit odd numbers can be formed using the digits 1,2,3,4,5,6 without using any digit more than once? Answered by Tyler Wood. 





Odds and evens in an n by n+1 table 
20100121 

From Shankar: The boxes of an n * (n+1) table ( n rows and n+1 columns) are filled with integers.
Prove that one can cross out several columns ( not all of them !) so that after this operation
all the sums of the numbers in each row will be even. Answered by Robert Dawson. 





Consecutive odd intergers 
20100106 

From keyanna: list five consecutive odd integers, starting with 3 Answered by Robert Dawson. 





Consecutive odd integers 
20091109 

From Erin: I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2
and so on, but if its odd then do the numbers change to odd ones? i don't know
the question is: the sum of four consecutive odd integers is 72. write an equation to model
this situation and find the values of the four integers Answered by Robert Dawson and Penny Nom. 





Four consecutive odd integers 
20091024 

From Tonya: the sum of four consecutive odd intergers 2008 what are the intergers Answered by Penny Nom. 





Rolling a six on the sixth roll 
20090504 

From Scott: What are the odds of rolling a die 6 times in a row and rolling a 6 only on the 6th try, but not any other time? And how is this calculated? Answered by Harley Weston. 





15 pigs in 4 pens 
20090422 

From Melissa: A farmer has 15 pigs. He wants to put them all into 4 pens, have an
odd number of pigs in each pen, and have no pigs left over. Also, he
isn't thinking about having any for dinner, as they are his pets.
How does he do it? Answered by Robert Dawson. 





Three consecutive odd integers 
20090402 

From Brian: Find the greatest of three consecutive odd integers if the product of the second and third is 8 more than 13 times the first. Answered by Robert Dawson. 





The odds against drawing a red queen 
20090315 

From tabyia: 7. The common deck of 52 cards has 26 black cards (13 spades and 13 clubs) and 26 red cards (13 hearts and 13 diamonds). Each suit consists of ace, king, queen, jack, ten, nine, eight, seven, six, five, four, three and deuce. 13in all.
A single card is chosen at random. Find the odds against its being a red queen?
How many cards will I have to draw to be absolutely certain that I have drawn three black cards Answered by Harley Weston. 





Three consecutive odd integers 
20090311 

From Susan: Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70 Answered by Penny Nom. 





Dividing the digits 1  9 into two groups 
20090209 

From donna: using the numbers 1 to 9 can you arrange these into 2 groups, both of which have the same total, and no you cant turn the 6 upside down Answered by Penny Nom. 





Three consecutive odd integers 
20081103 

From kim: Determine three consecutive odd integers such that twice the sum of the second and third is 29 less than 5 times the first. Answered by Penny Nom. 





Is it possible to a function to be both even and odd ? 
20080928 

From Mohammed: Is it possible to a function to be both ( Even and Odd ) Answered by Harley Weston. 





Is zero an even number, an odd number, or neither? 
20080804 

From Donna: Is zero an even number, an odd number, or neither? Why? Answered by Victoria West. 





A quadratic equation with odd coefficients 
20080415 

From Manashi: If p,q,r be any odd integers, then prove that the roots of the quadratic equation px^2+qx+r=0 can't be rational . Answered by Stephen La Rocque. 





Two consecutive odd numbers 
20080401 

From prinsilla: of all pairs of consecutive odd integers whose sum is greater than 75. find the pair whose sum is least? Answered by Stephen La Rocque. 





Two consecutive odd integers 
20080324 

From Jarrod: the sum of two consecutive odd integers is 24. Find the two integers Answered by Stephen La Rocque. 





Two consecutive odd positive integers 
20080312 

From Sarah: The sum of the squares of two consecutive odd positive integers is 74. What are th integers? Answered by Penny Nom. 





Some threedigit numbers 
20080305 

From Toni: The following is a word pattern problem listed on my son's homework:
write a set of threedigit numbers that contain one odd number and three even numbers.
This confused the both of us because that would make his number a four digit number, right?
please respond. Thanks. Answered by Penny Nom. 





3 consecutive odd integers 
20080228 

From Pat: For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals 85. Find the 3 consecutive odd integers. Answered by Penny Nom. 





Three consecutive odd integers 
20080124 

From daniel: find three consecutive odd integers such that three times the second minus the third is 11 more than the first.
help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while. Answered by Penny Nom. 





Why does an odd + odd = an even? 
20070906 

From austin: why does an odd + odd = an even? Answered by Penny Nom. 





Combining probabilities 
20070820 

From Arul: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2 , and 5/8 , respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem ? Answered by Stephen La Rocque. 





The odds of winning a contest 
20070729 

From Kevin: I have been asked by a customer in Missisauga to track down some odds of
winning a contest. In this contest, the last 4 digits of the winner's
driver's license number have to match the last 4 digits of a Harley VIN
number. There are 200 people maximum allowed into the drawing, 10,000 total
possible VIN combos. Would the odds be 1:50 or something other than that? Answered by Harley Weston. 





What are the odds that the selections were random? 
20070526 

From alan: An employer must select three people for layoff from three groups. Group 1 has 4 members and the oldest member is selected. Group 2 has 7 members and the oldest member is selected. Group 3 has 2 members and the younger is selected. Assuming equal qualifications, what are the odds that the selections were random vs. biased as to age? What is the formula to determine this? Answered by Penny Nom. 





Two consecutive odd numbers 
20070319 

From Alicia: The sum of two consecutive odd numbers is divisible by 4.
Can you make similar statements about the sum of three consecutive odd
numbers and of four consecutive odd numbers?
Generalize your findings.
I tried :
n= smallest odd number
therefore the next = n, n+2 and the second =n+4 and the third = n+6
Now n+ n+2+n+4+n+6/4
Please help I am not sure of this I am just trying Answered by Penny Nom. 





The square of an odd number 
20070316 

From Samantha: Is the square of an odd number always odd? Answered by Stephen La Rocque and Penny Nom. 





An odd function 
20070306 

From Dana: If g(x) has a domain of all real numbers, name one point on a graph and explain why it must be there. g(x) is an odd function. Answered by Penny Nom. 





21 pigs and only 4 pig pens 
20070111 

From Emma: i was given this pig pen problem. if there are 21 pigs and only 4 pig pens how can you distribute the pigs into the pens and have an odd number of pigs in each pen. it doesn't seem possible to me. i need help! Answered by Haley Ess. 





Three consecutive odd integers 
20070108 

From Emma: Find three consecutive odd integers such that the sum of the first and second is 27 less than 3 times the third. Answered by Stephen La Rocque. 





The Pythagorean theorem 
20061212 

From Beth: In a pythagorean theorem can the sides of a right triangle be three consecutive odd integers Answered by Stephen La Rocque. 





Factors 
20061122 

From Jacqueline: Why do the numbers 16,36,48,60,64,90 and 100 have an odd number of factors? Answered by Stephen La Rocque and Penny Nom. 





What is the probability that the sum of the two numbers is even? 
20061101 

From Ryan: 10 balls numbered 110 are in a jar. George reaches into the jar and pulls out a ball. Then Wally pulls out another ball. What is the probability that the sum of the two numbers is even? Answered by Haley Ess. 





An odd number of factors 
20061028 

From Anthony: What is the common name used for numbers that have an odd number of factors? This answer should be a two word answer only. Answered by Stephen La Rocque. 





Three consecutive odd numbers 
20061021 

From Pige: The sum of three consecutive odd numbers is 387. Find the numbers. Answered by Penny Nom. 





How many students are in the class? 
20061012 

From Lillian: There is one more boy than girls in the class, how many students in all? Answered by Stephen La Rocque. 





The odd numbers from 30 to 80 
20060921 

From Kieran: If you added all the odd numbers from 30 to 80, would the answer be even or odd? Explain.
I think it would be odd because I used this equation:
(30 x 5)+(40 x 5)+(50 x 5)+(60 x 5)+(70 x 5)+(25 x 5)=1325
I used the numbers for each set of ten 30 to 80 times 5 and the amount of the endings1,3,5,7,9 added, times 5. Is that right? Answered by Penny Nom. 





2row arrays 
20060906 

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





Oddman out coin tossing and probabilities 
20060427 

From Kalyan: When four people toss fair coins, what is the probability that in a given toss there will be one "odd man". That is one person whose coin does not have the same out comes as that of any other members? Answered by Stephen La Rocque. 





How to find the odds for a lottery jackpot 
20060412 

From Harvey: Is it best to use factorials to calculate the odds of winning a lottery, such as the MegaMillions that is popular in the US, or is there a better way? Answered by Stephen La Rocque. 





Probability of getting their stories straight 
20060405 

From Amy: Four students drive to school in the same car. They claim they were late because they had a flat tire. Assuming they did not have a flat tire what is the probability that they all would choose the same tire if asked which one was flat. Answered by Stephen La Rocque. 





Is zero even or odd? 
20060404 

From Aliya: I would like to know if zero is an odd number or even number. I remembered my kindergarten teacher saying it is an odd number. My mom and sister says it is even number. 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. 





The sum of n consecutive integers 
20051127 

From Craig:
If 875 is expressed as the sum of n consecutive integers (n > 1), then the number
of possible values of n is?
Possible Answers:
A) 15
B) 8
C) 7
D) 16
E) 4
Answered by Penny Nom. 





Numbers with exactly 5 divisors 
20051123 

From Mary Lou: Show the 10 numbers with exactly 5 divisors. Answered by Penny Nom. 





When will x^2+xy+(yx) be even? 
20051108 

From Lana: If x and y are integers, when will x squared+xy+(yx) be even? Answered by Penny Nom. 





Why is zero even? 
20051108 

From Lauren: A child in my class if having trouble with the concept of zero being an even number, I have talked with her about its zero because it is a multiple of 2, any other suggestions? Answered by Paul Betts. 





Seven consecutive reds in roulette 
20050904 

From Joe: I know that the odds are a little less than 50% for either black or red comming up on a spin of the roullette wheel. My question is what are the odds of red or black comming up 7 times in a row? 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. 





Probabilities in poker 
20041104 

From Ben: Please can someone tell me the odds of getting a royal flush while playing texas hold em.
Please can you also let us know the odds of a royal flush while playing texas hold em if you must be dealt two of the needed cards. Answered by Chris Fisher. 





Sums and differences 
20040210 

From David: The sum of two whole numbers is 63. The difference between the numbers is 10. Find all the possible pairs. Answered by Claude Tardif and Penny Nom. 





Is zero even? 
20040107 

From A secretary at an elementary school: Is zero an even number? Answered by Penny Nom. 





Two row arrays 
20030903 

From Madalyn: My question is, what are #'s that can not be arranged in two row arrays called? Answered by Penny Nom. 





Two precalculus problems 
20030804 

From Kate:
Please help me verify the identity: cos2x(sec2x1)=sin2x Also I am having trouble withdetermining whether f(x) is odd, even, or neither f(x)=x3x Answered by Penny Nom. 





The area of an odd shaped piece of property 
20030724 

From Barry: What is the formula for figuring the square footage of an odd shaped piece of property? Answered by Penny Nom. 





Would it be worth paying $20K for 4 chances... 
20030113 

From Steve:
If I've got 4 chances to to achieve X goal, and in each chance that I have I've got a 65% chance of achieving this goal, what is my overall probablity of achieving this goal? Also, what would it be after each of my 4 chances (i.e., for my 2nd chance, would it be (.65 * (.65*.65)? I've forgotten some basic probablity theories, and would appreciate any help on this. With the probablities above, would it be worth paying $20K for 4 chances to achieve the goal or $8.5K for only 1 chance to acheive the goal? (at 65% probability) Answered by Andrei Volodin. 





Odd and even 
20021217 

From Martin: I am a graduate engineer trying to teach single digit addition to my 8 year old granddaughter. My questions follow. Assume a child does not know what multiplication and division are. Assume the child knows how to count from 0 to 10 How do you explain that 2, 4, 6, 8 and 10 are even numbers And 1, 3, 5, 7 and 9 are odd numbers And these three facts?  when you add two even numbers, the answer is even
 when you add two odd numbers, the answer is even
 when you add an even number and an odd number, the answer is odd?
Can all of these be reasoned out, without using the concepts of multiplication or division? Answered by Diane Hanson. 





Place six numbers around a triangle 
20020719 

From Monika: I need to place six numbers around a triangle, as such that one number is on each corner, and one number on each side making three numbers in one line, adding up to two hundred exactly. The number I have to use are, 40, 50, 60, 70, 80, 90. I have to use each one once, there for, each number cannot be repeated. Answered by Claude Tardif and Chris Fisher. 





Pigs in pens 
20020710 

From Shannon: A farmer has 21 pigs and 4 pens, he must put an odd number of pigs in each pen, how does he do it? Answered by Penny Nom and Chris Fisher. 





Odd plus even is odd 
20011014 

From James: Why is the sum of an odd number and an even number always odd? Answered by Peny Nom. 





15 mice in 4 cages 
20011008 

From Chelsea: How can you fit 15 mice into 4 cages with an odd number of mice in each cage? Answered by Claude Tardif and Harley Weston. 





Probabilities and dice. 
20010504 

From Carmen: Hi! My name is Carmen! I am a member of a grade 5 class in Edmonton, AB. We were talking about probability in math, and I was wanted to know what the probability (odds) of rolling two sixes would be rolling two dice? If it is not to diffucult could you tell me what the probability (odds) of rolling any number with two dice were? Answered by Andrei Volodin and Penny Nom. 





Is there an odd and even function? 
20010302 

From Saima: Is there a function that is both even and odd at the same time? In other words, is there a function that can pass the yaxis, xaxis, and origin symmetry test? Answered by Claude Tardif and Penny Nom. 





The odds of winning 
20010209 

From Anna: The odds of winning in a game are 3 out of 10. How many times would one have to play the game in order to be sure they would win? Answered by Leeanne Boehm. 





14, with 5 ODD numbers 
20010123 

From Robyn Ernst: How can you get 14, with 5 ODD numbers? Answered by Claude Tardif. 





Three consecutive odd integers 
20000818 

From Wallace: A sixdigit integer XYXYXY, where X and Y are digits is equal to five times the product of three consecutive odd integers. Determine these three odd integers. Answered by Paul Betts. 





Odds and combinations 
20000510 

From Lucy: If the odds are 1/15 of winning, what is the probability? if c 5! 3! How does it equal 10? Answered by Harley Weston. 





Probability and odds 
20000505 

From Leah: The chances of rain on friday, saturday, and sunday are 20%, 30%, and 50% respectively. what are the odds it will rain all three days? Answered by Harley Weston. 





Is zero an even or odd number? 
20000206 

From Christian Hansen: On a list I run, someone posted that 02022000 was the first date since 2808888 where all the digits were even. Of course, this provoked a discussion of whether zero was odd, or even, or neither. I remember reading that, for symmetry's sake, it is considered by mathematicians to be even. Any thoughts? Answered by Patrick Maidorn. 





Two algebra problems 
19991217 

From Michael Standfest: If x+4 is a factor of 2x^{4}+kx^{3}3kx^{2}+6x40, find k and Prove that n^{2}n is even for all n, using the proof of contradiction Answered by Penny Nom. 





An odd number of factors 
19991022 

From Melissa: What is the common name used for numbers that have an odd number of factors? What is the least positive integer that has exactly 13 factors? Answered by Penny Nom. 





A Multiple Choice Test 
19990831 

From Cintra Ramnarine: I have ten questions. There are two multiple choice answers to each question. What are the chances of answering all questions correctly. Answered by Harley Weston. 





Even and Odd Function 
19990617 

From Kent: There is one function with the domain of all real numbers that is both even and odd. Please give me the answer to this question before I go insane. Answered by Penny Nom. 





Evens and odds 
19990504 

From Emily Hays: My name is Emily Hays, I am in the 6th grade and my teacher gave me some extra probelms to see if I could solve them. She can't find the KEY and I can't figure out the probelm so she suggested I email you guys to see if you could help us. Here's the Problem: The numbers 1,2,3...,1999 are written on the blackboard in the classroom. Evertime the teacher enters the room he chooses two numbers on the blackboard, say a & b, with a> or equal to b, then he erases them and writes the difference ab somewhere on the blackboard. After this procedure is carried on 1998 times, there will be only one number left on the blackboard. Prove the last remaining number must be even. I hope you can help us! Answered by Chris Fisher and Harley Weston. 





Zero 
20010315 

From Alexandre: j'aimerais beaucoup savoir si le chiffre zéro est considéré comme étant soit:  pair
 impair
 pair et impair ŕ la fois
 ni pair ni impair.
Answered by Claude Tardif. 

