Posted in May 2012

#math trivia #April3 solution

Burt Kaliski Jr. (@modulomathy) 4/3/12 7:34 AM #math trivia for #April3: day*month = year today. How many other days does this happen in ’12? Is there any year with more “product” days? This problem, unlike most (but like the next one) is about the actual date, not the day-number (which would be #94). The other … Continue reading

#math trivia #93 solution

Burt Kaliski Jr. (@modulomathy) 4/2/12 9:45 AM #math trivia for #April2: #93 can be checked for divisibility by 3 by adding the digits and checking the sum. Why does this test work? The classic test for divisibility by 3 is to add the digits of a number and test if the sum is divisible for … Continue reading

#math trivia #92 solution

Burt Kaliski Jr. (@modulomathy) 4/1/12 10:35 PM #math trivia for #April1: #92 = 7*13+1, so April is congruent to January; both start on Sunday. What other months are congruent this year? The answer is a simple matter of modular arithmetic. Reduced modulo 7, the lengths of the 12 months in a leap year follow the … Continue reading

#math trivia #91 solution

Burt Kaliski Jr. (@modulomathy) 3/31/12 1:21 PM #math trivia for #March31: #91 is XCI in Roman numerals. What other numbers this year only use the Roman powers of 10 (I, X and C)? A Roman numeral can have as many as three consecutive Is, Xs and Cs, so a number in the 0s, 100s, 200s … Continue reading

#math trivia #90 solution

Burt Kaliski Jr. (@modulomathy) 3/30/12 8:01 AM #math trivia for #March30: #90 has four pairs of consecutive divisors: (1,2)(2,3)(5,6)(9,10). What’s the next number with at least four? The next number is 120: (1,2)(2,3)(3,4)(4,5)(5,6) — five pairs of consecutive divisors.

#math trivia #89 solution

Burt Kaliski Jr. (@modulomathy) 3/29/12 7:10 PM #math trivia for #March29: #89 can be constructed from the numbers 8 and 9 with + and * operations. How? What if you also had – and / ? With just addition and multiplication, the simplest construction is 89 = 8*9 + 8 + 9. A longer form … Continue reading

#math trivia #88 solution

Burt Kaliski Jr. (@modulomathy) 3/28/12 2:23 PM #math trivia for #March28: #88 is the sum of three squares (not necessarily distinct) What are they? One way to do it is with 49, 25 and 4. Another is with 36, 36 and 16. It turns out that every number can be expressed as the sum of … Continue reading

#math trivia #87 solution

Burt Kaliski Jr. (@modulomathy) 3/27/12 7:44 AM #math trivia for #March27: #87 is three times a prime. How many numbers of this form this year? (As usual, looking at numbers 1-366.) This time it’s the number of primes up to 122: π(122) = 30.

#math trivia #86 solution

Burt Kaliski Jr. (@modulomathy) 3/26/12 8:55 AM #math trivia for #March26: #86 is two times a prime. How often does this happen in a leap year? (Including 2*2=4.) The equivalent question is, how many primes are between 1 and 183? This value is denoted π(183), the number of primes less than or equal to 183. … Continue reading

#math trivia #85 solution

Burt Kaliski Jr. (@modulomathy) 3/25/12 10:28 AM #math trivia for #March25: #85 is 55 base 16. How many “two of a kinds” base 16 in a leap year? (Compare #66.) “Two of a kind” means that two of the digits are the same, base 16. This happens 15 times from 11 to ff base 16, … Continue reading