# Posted in June 2012 …

## #math trivia #121 solution

#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 #120 solution

#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

## #math trivia #116 solution

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

## #math trivia #114 solution

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

## #math trivia #117 solution

#math trivia for #April26: #117 is one of 40 day-numbers divisible by 9 this year. How many also have digits that add up to 9? — Burt Kaliski Jr. (@modulomathy) April 26, 2012 Any number whose digits add up to a multiple of 9 is divisible by 9, and vice versa. Most of the day-numbers … Continue reading

## #math trivia #118 solution

#math trivia for #April27: #118 is the sum of three squares (not necessarily distinct) in two different ways. What are they? — Burt Kaliski Jr. (@modulomathy) April 27, 2012 The two ways are: 118 = 1+36+81 118 = 9+9+100 One way to find the answers is to start by observing that at least one of … Continue reading

## #math trivia #119 solution

#math trivia for #April28: #119 is the product of two primes differing by 10. Any other day-numbers of this type? — Burt Kaliski Jr. (@modulomathy) April 29, 2012 In other words, are there other day numbers of the form p*q where q = p+10 and p and q are both prime? The value of p … Continue reading

## #math trivia #115 solution

Burt Kaliski Jr. (@modulomathy) 4/24/12 6:54 PM #math trivia for #April24: #115 is 5*23; digit-sum of each prime factor is the same. What other day-numbers this year does this happen? The other possibilities are, by digit-sum, — 2: 4, 22, 202 — 3: 9 — 4: 169 — 5: 25, 115, 205 — 6: none … Continue reading

## #math trivia #113 solution

Burt Kaliski Jr. (@modulomathy) 4/22/12 4:26 PM #math trivia for #April22: #113 is 16 weeks and 1 day, both squares. How many days of the year does this happen? The pattern happens twice during the week preceded by a square number of full weeks. There are eight square numbers between 0 and 52 inclusive, so … Continue reading

## #math trivia #112 solution

Burt Kaliski Jr. (@modulomathy) 4/21/12 3:27 PM #math trivia for #April21: #112 is four times a perfect number. Does that make it more or less abundant? Is there a general rule? The divisors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112. The sum of the divisors less than the … Continue reading