# Posted in May 2012 …

## #math trivia #73 solution

Burt Kaliski Jr. (@modulomathy) 3/13/12 7:42 AM #math trivia for #March13: #73 as a modulus gives square roots to -1. Solve x^2+1 = 0 (mod 73) where x is an integer between 0 and 72. One way to find the square root is by trial and error, looking for the smallest integer congruent to 72 … Continue reading

## #math trivia #72 solution

Burt Kaliski Jr. (@modulomathy) 3/12/12 10:48 AM #math trivia for #March12: #72 is both a sum and a difference of squares. What are the squares? The sum of squares is 36+36. The difference has several possibilities: 81-9, 121-49, 361-289. For further discussion, see the solution to #68.

## #math trivia #71 solution

Burt Kaliski Jr. (@modulomathy) 3/11/12 6:02 PM #math trivia for #March11: #71 is closest integer to sqrt(5000) — average 2 weeks per thousand. What’s the average for the next five? The “next five” here refers to the next five thousand, and the question is asking for the average number of weeks per thousand from sqrt(5000) … Continue reading

## #math trivia #70 solution

Burt Kaliski Jr. (@modulomathy) 3/10/12 2:27 PM #math trivia for #March10: #70 is one of three tricomposites this month (products of three distinct primes). What are the other two? The three prime factors of 70 are, of course, 2, 5, and 7. March’s day-numbers range from 60 to 91. The other tricomposites among them are … Continue reading

## #math trivia #69 solution

Burt Kaliski Jr. (@modulomathy) 3/9/12 7:52 AM #math trivia for #March9: #69 can be expressed as the sum of three primes many ways, incl. 23+23+23. What are the other ways? The primes must all be odd, because 2+2 would have to be added to 65, which is not prime. The largest of the primes must … Continue reading

## #math trivia #68 solution

Burt Kaliski Jr. (@modulomathy) 3/8/12 7:21 AM #math trivia for #March8: #68 is both the sum of squares and the difference of squares. What are the squares? The sum of squares is 64+4, or 8^2+2^2. The difference is 324-256, or 18^2-16^2. General rule for the difference of squares: if an integer N can be expressed … Continue reading

## #math trivia #67 solution

Burt Kaliski Jr. (@modulomathy) 3/7/12 8:17 AM #math trivia for #March7: #67 divided by 366 = 1/p – 1/q + 1/r for p, q, r prime. What are the values of p, q and r? Start by expressing 67/366 as a sum of fractions: 67/366 = 61/366 + 6/366 = 1/6 + 1/61. The second … Continue reading

## #math trivia #66 solution

Burt Kaliski Jr. (@modulomathy) 3/6/12 7:14 AM #math trivia for #March6: #66 is “two of a kind”. What are the odds of getting “two of a kind” in a leap year? (Ignore leading 0s) The question is asking for the number of integers between 1 and 366 that have exactly two of some digit in … Continue reading