Burt Kaliski Jr. (@modulomathy) 4/20/12 5:23 PM #math trivia for #April20: #111 is a prime in every base less than 10, except for which two? The base-10 values corresponding to 111 in bases 1 to 9 are 3,7,13,21,31,43,57,73,91 There are actually three non-primes in this list, the ones corresponding to bases 4, 7, and 9. … Continue reading →

#math trivia for #April19:#110 is 10*11, 2 more than 9*12, 6 more than 8*13, 12 more than 7*14, etc.What’s the pattern? — Burt Kaliski Jr. (@modulomathy) April 19, 2012 Let n be the index of the term, starting at 0.  The terms follow the pattern:   110 = (10-n)*(11+n) + n*(n+1) In other words, for … Continue reading →

#math trivia for #April17: #108 equals 2^2 * 3^3. What’s the next number that can be expressed as a product of x^x terms (x > 1)? — Burt Kaliski Jr. (@modulomathy) April 17, 2012 If a multi-term product is required, then the next number is 2^2 * 4^4, or 1024. If “products” with just one … Continue reading →

#math trivia for #April16: #107 is the square root of 11449. Is there another number whose square has the form aabbc? — Burt Kaliski Jr. (@modulomathy) April 17, 2012 Assuming that a is non-zero, the square root must be a three-digit number.  Let xyz be the digits of a number N, so that N = … Continue reading →

#math trivia for #April15:#106 is the smallest three-digit number that’s twice a prime.What’s the largest one? — Burt Kaliski Jr. (@modulomathy) April 15, 2012 The largest three-digit number that’s twice a prime is equal to two times the largest prime less than 500, which is 499.  The answer is 998.

#math trivia for #April14: #105 sets a new record for number of odd divisors. What is it and when will it be broken again? — Burt Kaliski Jr. (@modulomathy) April 14, 2012 There are eight odd divisors of 105:  1, 3, 5, 7, 15, 21, 35 and 105.  The total of eight makes sense given … Continue reading →

#math trivia for #April13: Second #FridayThe13th this year. Is there a third?What’s the most a year can have? The fewest? — Burt Kaliski Jr. (@modulomathy) April 13, 2012 This one is related to the answer to #92. The starting days of the month, as noted in that answer, have the following modular values (relative to January 1) … Continue reading →

#math trivia for #April12:#103 and 263 are primes that sum to 366.How many other ways can 366 be expressed as the sum of two primes? — Burt Kaliski Jr. (@modulomathy) April 12, 2012 There are 17 other ways (determined with the help of a spreadsheet): 7 359 13 353 17 349 19 347 29 337 … Continue reading →

#math trivia for #April11:  #102 contains three consecutive digits.  How many other numbers 100-366 have this property? — Burt Kaliski Jr. (@modulomathy) April 12, 2012 The simplest way is probably to look at the eight different possible sets of digits involved: 0,1,2:  102, 120, 201, 210 (4 ways) 1,2,3:  123, 132, 213, 231, 312, 321 … Continue reading →