#math trivia for #May4: #125 divides 1000. What other day-numbers divide a power of 10? What’s the general pattern these numbers follow? — Burt Kaliski Jr. (@modulomathy) May 4, 2012 The day-numbers that divide a power of 10 (and the power they divide) are: 1 — 1 2 — 10 4 — 100 5 — … Continue reading →

#math trivia for #May3:  How many day-numbers, like #124, have the property that the no digit is larger than the one’s digit? — Burt Kaliski Jr. (@modulomathy) May 4, 2012 This is a little different than the answer to #123, where the digits had to be in increasing order.  (And to be clear, the “the” … Continue reading →

#math trivia for #May2:  The digits of #123 are in increasing order:  1 < 2 < 3.  How many other numbers 1-366 have this arrangement? — Burt Kaliski Jr. (@modulomathy) May 2, 2012 We’ll start by assuming that single-digit numbers have their single digit in increasing order.  9 numbers so far. Among the two-digit numbers, … Continue reading →

#math trivia for #May1: #122 reversed is #221, also a day-number (1-366). How many day-numbers have this property? (Leading 0s not allowed.) — Burt Kaliski Jr. (@modulomathy) May 1, 2012 All of the one-digit day-numbers, 1-9, when reversed, are themselves, so have the property.  That’s 9. All of the two-digit day-numbers, 10-99, when reversed, are … Continue reading →

#math trivia for #June7:  #159 is the product of 3 and 53, two primes with the same last digit. What other day-numbers have this property? — Burt Kaliski Jr. (@modulomathy) June 8, 2012 One of the primes must be less than or equal to the square root of 366, i.e., 19 or less.  We can … Continue reading →

#math trivia for #April30: #121 is the square of 11 in every base > 1 except which one? What’s the square of 11 in that base? — Burt Kaliski Jr. (@modulomathy) April 30, 2012 The only base > 1 in which 121 is not a square of 11 is the base in which 121 is … Continue reading →

#math trivia for #April29: #120 has 16 positive divisors, more than any day-number so far this year. Which day-numbers this year have more? — Burt Kaliski Jr. (@modulomathy) April 30, 2012 One way to calculate the number of positive divisors of 120 is to consider its factors: 120 = 2^3 * 3 * 5 There … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/25/12 6:43 PM #math trivia for #April25: #116 is the sum of two squares in base 10. Are there any other bases for which this is true? The value 116 is the sum of squares in any base in which 16 is also a square, because 100 is a square in … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/23/12 3:25 AM #math trivia for #April23: #114 is a product of three primes. How many other numbers 1-366 have this form? What if prime powers are allowed? The first form to consider is p*q*r where p, q, and r are distinct primes. The numbers with this form in the range … Continue reading →