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#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 →

#math trivia for #February19: #50 is the largest “coin” dividing into a 100-unit “dollar”. What are the other “coins” for this “dollar”? — Burt Kaliski Jr. (@modulomathy) February 19, 2012 For the purposes of this problem, a “coin” should be taken as a a divisor of 100 that is smaller than 100.  Even though 100 … Continue reading →

#math trivia for #February18: #49 is the first composite that Eratosthenes sieves with a prime other than 2, 3 or 5. What’s the next one? — Burt Kaliski Jr. (@modulomathy) February 18, 2012 The Sieve of Eratosthenes is an ancient algorithm for separating prime numbers from composites.  Suppose we want to find all the primes … Continue reading →

#math trivia for #February17: #48 is very abundant — its divisors add up to 124. How do you go from 48 = 16*3 to 124 = 31*4? — Burt Kaliski Jr. (@modulomathy) February 17, 2012 A perfect number n one whose smaller divisors add up to n.  The first two perfect numbers are 6 (smaller … Continue reading →

#math trivia for #February16: 47 is the third prime this “decade” (the 40s). Why are the 10s, 40s and 70s so popular for primes? — Burt Kaliski Jr. (@modulomathy) February 16, 2012 The 10s, 40s and 70s each have at least three primes: 10s:  11, 13, 17,  19 40s:  41, 43, 47 70s:  71, 73, … Continue reading →