#math trivia for #February28:#59 and 61 are twin primes. What property of 60 makes this possible? (Hint:29 and 31 were also twins.) — Burt Kaliski Jr. (@modulomathy) February 28, 2012 The property of 60 that makes adjacent twin primes possible is that 60 is divisible by 6. If 60 were not divisible by 2, then … Continue reading →

#math trivia for #February27: #58 is the 7th in the series 2 5 10 17 28 41 58. What’s the 8th? — Burt Kaliski Jr. (@modulomathy) February 27, 2012 A good starting point for answering a question about the next term in a series is to look at the differences between successive terms, which in this case is: 2 3 … Continue reading →

#math trivia for #February26: #57 = 3*19 — a product using each odd digit once. Are there any other products of this form? — Burt Kaliski Jr. (@modulomathy) February 26, 2012 Let’s think about what a solution might look like. The general form needs to be ab = c*de where a, b, c, d and … Continue reading →

#math trivia for #February25:  #56 is a product of consecutive numbers: 56 = 7*8. And 56 = ((7+8)^2)-1)/4.  What’s the general formula? — Burt Kaliski Jr. (@modulomathy) February 25, 2012 Replacing 7 with x and 8 with x+1 gives the general formula x(x+1) = ((x+(x+1))2-1)/4. Replacing x+(x+1) with 2x+1 on the right hand side gives … Continue reading →

#math trivia for #February24: #55 is the 10th in the series 1 1 2 3 5 8 13 21 34 55. What’s the 11th and what’s the series? — Burt Kaliski Jr. (@modulomathy) February 24, 2012 The next term is 89, and the series is the Fibonacci Series. New terms follow a simple rule:  They’re … Continue reading →

#math trivia for #February23: #54 is halfway between a #cube and a #square, two different ways.  What are they?  (Positive numbers only.) — Burt Kaliski Jr. (@modulomathy) February 23, 2012 One solution is 27 (= 33) and 81 (= 92). The other is 8 (=23) and 100 (=102). The problem can be solved by trial … Continue reading →

#math trivia for #February22: #53 is surrounded by more composites than any prime so far.  How many immediate neighbors of 53 aren’t prime? — Burt Kaliski Jr. (@modulomathy) February 22, 2012 Ten immediate neighbors of 53 aren’t prime: 48 49 50 51 52 … 54 55 56 57 58 The gaps between 47 and 53 … Continue reading →

#math trivia for #February21: Day #52 — 1/7th of the way through the year. Whenwill it be 1/6th? — Burt Kaliski Jr. (@modulomathy) February 21, 2012 An easy one today:  One sixth of the way through a 366-day leap year is exactly 61 days, a milestone reached on March 1. In a non-leap year, the … Continue reading →

#math trivia for #February20: #51 is 33 base 16. Approximately what fraction is 33 base 16 of 100 base 16? — Burt Kaliski Jr. (@modulomathy) February 20, 2012 33 is just under one third of 100 base 10 — but the question is asking about base 16. There are two approaches to solve this one.   … Continue reading →