#math trivia #244 solution

#math trivia for #September1: #244 is the integer after (8/12)*365. Which other months start on the “right” day-number for the month? — Burt Kaliski Jr. (@modulomathy) September 2, 2013 The “right” day-number for month number M to start on, based on the first sentence, is apparently the integer after ((M-1)/12)*365.  The logic is that each … Continue reading →

#math trivia #172 solution

#math trivia for #June20: #172 has three digits that add to 10. How many numbers 100-999 do? — Burt Kaliski Jr. (@modulomathy) June 21, 2012 This is one of those problems that gets easier by recursion.  In particular, for each of the possible first digits, a, of the three-digit number, we just need to know … Continue reading →

#math trivia #243 solution

#math trivia for #August31: #243 is 300 in base 9. Which other day-numbers (1-365) can be represented as 300 in some base? — Burt Kaliski Jr. (@modulomathy) September 1, 2013 If a number is represented as 300 base B, then it’s equal to 3*B2.  The answer to the question can thus be found by enumerating … Continue reading →

#math trivia #171 solution

#math trivia for #June19: #171 is one of five palindrome day-numbers (same forward and reverse) divisible by 9. What are the others? — Burt Kaliski Jr. (@modulomathy) June 20, 2012 The sum of the digits of a number divisible by 9 is itself divisible by 9; this follows from the fact that powers of 10 … Continue reading →

#math trivia #242 solution

#math trivia for #August30: #242 has the form abc, a+c=b. Are all such three-digit numbers also divisible by 11? Vice versa? — Burt Kaliski Jr. (@modulomathy) August 31, 2013 Question 1:  Are all three-digit numbers having the form abc where a+c=b divisible by 11? Answer:  Yes. Proof:  Let x be a number of the specified … Continue reading →

#math trivia #170 solution

#math trivia for #June18: #170 can be factored three different ways into the form (a+b)*(c+d) where a, b, c, d are squares. What are they? — Burt Kaliski Jr. (@modulomathy) June 19, 2012   Start by listing the possible factorizations of 170: 1*170 2*85 5*34 10*17 Among the eight factors, the ones that can be … Continue reading →

#math trivia #241 solution

#math trivia for #August29: #241 and #239 are twin primes. Does the fact that #240 is highly composite make this more likely? — Burt Kaliski Jr. (@modulomathy) August 30, 2013 A number is either prime or it isn’t, so the behavior of an adjacent number can’t make it more or less likely that a given … Continue reading →

#math trivia #169 solution

#math trivia for #June17: #169 is one of eight day-numbers that are squares of primes. What are the others? — Burt Kaliski Jr. (@modulomathy) June 18, 2012 Recall that “day-numbers” are integers between 1 and 366 — the numbers of the days of the year (366 is included because the problem was given during a … Continue reading →

#math trivia #240 solution

#math trivia for #August28: #240 is highly composite: it has more divisors than any smaller number. How many? What was the previous record? — Burt Kaliski Jr. (@modulomathy) August 29, 2013 The number 240 has 20 divisors:  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, … Continue reading →

#math trivia #168 solution

#math trivia for #June16: #168 is 2^3 * 3^1 * 7^1. How many positive divisors does it have? — Burt Kaliski Jr. (@modulomathy) June 16, 2012 The number of positive divisors of 168 is 16. Given the factorization of 168, we know that any positive divisor must have the form 2i * 3j * 7k … Continue reading →