# Filed under Math Trivia …

## #math trivia solution: What are the chances that a class of 20 has 10 girls and 10 boys?

#math trivia: If girls and boys are equally represented in the school population, what are the chances that a class of 20 has 10 of each? — Burt Kaliski Jr. (@modulomathy) October 16, 2012 This is another combinatorics problem. Each seat in the class will be occupied either by a girl or a boy. The … Continue reading »

## #math trivia solution: The principal chooses one student from each of 5 classes …

#math trivia: The principal chooses one student from each of 5 classes of 20 for a project team. How many different “rosters” are possible? — Burt Kaliski Jr. (@modulomathy) October 1, 2012 The number of possible rosters is 3.2 million. This assumes that it doesn’t matter in what order the students are chosen for the … Continue reading »

## #math trivia solution: The five classes eat lunch at separate times …

#math trivia: The five classes eat lunch at separate times. Every day their times are in a different order. How long can this go on? — Burt Kaliski Jr. (@modulomathy) September 17, 2012 There are 5*4*3*2*1 = 120 different possible orders in which the five classes can eat lunch, so this can go on for … Continue reading »

## #math trivia solution: The 20-student class gets the flu …

#math trivia: The 20-student class gets the flu. Every day a different prime number of students is out sick. For how long can this go on? — Burt Kaliski Jr. (@modulomathy) September 10, 2012 There are eight different prime numbers less than or equal to 20 (2, 3, 5, 7, 11, 13, 17 and 19), … Continue reading »

## #math trivia solution: Two friends got in the same class …

#math trivia: The two friends got in the same class. Seats are assigned randomly, 4 rows of 5. What are the chances that they sit together? — Burt Kaliski Jr. (@modulomathy) September 3, 2012 The chances that the two friends are seated next to each other is 8/95.  This can be calculated as follows: The … Continue reading »

## #math trivia solution: 100 students are assigned randomly …

#math trivia: 100 students are assigned randomly to 5 classes of equal size. What are the chances that two friends get in the same class? — Burt Kaliski Jr. (@modulomathy) August 28, 2012 The chances that two friends get in the same class is 19 out of 99. If the classes didn’t have to be … Continue reading »

## #math trivia #134 solution

#math trivia for #May13:  #134 and its prime divisors (67, 2) have no common digits.  When did this last happen?  When will it happen again? Answer:  This is a fun problem that can be solved with by trial-and-error moving forward and backward from 134, using some properties of factorizations to shorten the search. Clearly, a … Continue reading »

## #math trivia #133 solution

#math trivia for #May12:  #133 has the form xyz where xyz is one more than a multiple of yz (133 = 4*33+1).  Which other day-numbers do? Answer:  If xyz is one more than a multiple of yz, then x00 = xyz = yz is also one more than a multiple of yz.  This means that … Continue reading »

## #math trivia #132 solution

#math trivia for #May11: #132 can be expressed in three ways as the product of positive integers x, y where x-y is a square.  What are they? Answer:  Consider the possible factorizations of 132 into x*y: 132*1 66*2 44*3 33*4 22*6 12*11 The three factorizations where x-y is a square are 66*2, 22*6, and 12*11.

## #math trivia #131 solution

#math trivia for #May10:  #131 is a prime, 13 is a prime, and 31 is a prime.  For what other day-numbers xyz are xyz, xy and yz all prime? Answer:  This is a good pattern matching problem.  The shortest approach is probably to look at prime xy values and see which z’s work.  We’ll allow … Continue reading »