Posted in May 2012

#math trivia #84 solution

Burt Kaliski Jr. (@modulomathy) 3/24/12 10:06 AM #math trivia for #March24: #84 is 2^2*3*7. How many divisors does it have and why? Compare solution to #42: wp.me/p2ef3C-f There are 12 divisors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84. Here’s why the number is 12: Each divisor must … Continue reading

#math trivia #83 solution

Burt Kaliski Jr. (@modulomathy) 3/23/12 11:49 AM #math trivia for #March23: #83 has a “signature” of (1,2,3,6) modulo the primes (2,3,5,7). What’s the next number with this signature? Because 2, 3, 5 and 7 are distinct primes (pairwise relatively prime would be sufficient), the signature repeats with a period equal to the product of the … Continue reading

#math trivia #82 solution

Burt Kaliski Jr. (@modulomathy) 3/22/12 7:50 AM #math trivia for #March22: #82 is one of several numbers whose digits sum to 10. How many others are there this year? How many overall? In the range 1 to 366, there are 35 numbers whose digits sum to 10: — 9 numbers between 1 and 99: 19, … Continue reading

#math trivia #81 solution

Burt Kaliski Jr. (@modulomathy) 3/21/12 2:54 PM #math trivia for #March21: #81 is a square, and the sum of its digits is a square. What other days this year have this property? The one-digit squares all have this property: 1, 4, 9. Among the 15 other day-numbers not already mentioned that are squares, the ones … Continue reading

#math trivia #80 solution

Burt Kaliski Jr. (@modulomathy) 3/20/12 11:06 AM #math trivia for #March20: #80 has the form x^4-1 for x > 2 so must have at least three nontrivial divisors. What are they, and why three? The nontrivial divisors of 80 (those other than 80 or 1) are 2, 4, 5. 8, 10, 16, 20, and 40. … Continue reading

#math trivia #79 solution

Burt Kaliski Jr. (@modulomathy) 3/19/12 10:37 PM #math trivia for #March19: #79 has one of the highest digit sums of any two-digit prime: 7+9=16. Which two-digit prime has a higher sum? The only two-digit prime with a higher digit sum than 79 is 89. Indeed, the only two-digit numbers with a higher digit sum than … Continue reading

#math trivia #78 solution

Burt Kaliski Jr. (@modulomathy) 3/18/12 8:47 PM #math trivia for #March18: #78 was a common format for what 20th century media? What other numbers were common? (NB: Not #numbertheory!) The answer to this non-number-theoretic piece of trivia is the 78-RPM record. I remember having a record player at one time with three speeds: 33, 45, … Continue reading

#math trivia #77 solution

Burt Kaliski Jr. (@modulomathy) 3/17/12 2:12 PM #math trivia for #March17: #77 is a product of two consecutive primes — fourth such product this year. How many more are there in 2012? There can’t be that many more, because we’re already up to 7*11, and the square root of 366 — the largest day-number this … Continue reading

#math trivia #76 solution

Burt Kaliski Jr. (@modulomathy) 3/16/12 1:12 PM #math trivia for #March16: #76 is one of the more common two-digit endings of squares between 1 and 999. What endings are more common? This problem looks at the range of numbers from 1 to 999 rather than the usual day-number range of 1 to 366 for a … Continue reading

#math trivia #74 solution

Burt Kaliski Jr. (@modulomathy) 3/14/12 3:17 PM #math trivia for #March14: Happy #PiDay — a much more fascinating number to ponder today than #74 Indeed, π, the ratio between the circumference of a circle and its diameter, is one of the most famous and useful numbers in mathematics. The closest approximation to π to two … Continue reading