#math trivia #97 solution

Burt Kaliski Jr. (@modulomathy) 4/6/12 9:42 AM #math trivia for #April6: #97 is the largest prime less than 100. Are primes more likely than average to occur very close to a power of 10? “Average” here can be understood to refer to the probability that a random number “in the vicinity” (but not necessarily “very … Continue reading →

#math trivia #96 solution

Burt Kaliski Jr. (@modulomathy) 4/5/12 8:25 AM #math trivia for #April5: #96 ties record for prime factors counting repeats (6), but doesn’t match record for divisors (12). Why not? The six prime factors of 96, counting repeats, are 2, 2, 2, 2, 2, and 3. This ties 64, which is the product of six 2s. … Continue reading →

#math trivia #April4 solution

Burt Kaliski Jr. (@modulomathy) 4/4/12 7:14 PM #math trivia for #April4: How many times this year do month and day both divide into year (’12)? In what year does this happen most often? Another non-day-number problem, similar to #April3. Both day and month divide into year 36 times in ’12: whenever both are among the … Continue reading →

#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 →