#math trivia for #September28: #271 is a permutation of digits 1, 2, 7. Which other day-numbers (1-365) are a permutation of these digits? — Burt Kaliski Jr. (@modulomathy) September 29, 2013 There are six possible permutations of any three distinct digits; in this case, the six possibilities are: 127 172 217 271 712 721 However, … Continue reading

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## #math trivia #163 solution

#math trivia for #June11: #163 has three different digits where two (1,3) divide into the other (6). What’s the next number like this? — Burt Kaliski Jr. (@modulomathy) June 12, 2012 The next number with three different digits where two divide into the other is 182. Several numbers in between satisfy the divisibility requirement, but … Continue reading

## #math trivia #263 solution

#math trivia for #September20: #263 has no digits in common with its base-N representation for which N < 10? — Burt Kaliski Jr. (@modulomathy) September 21, 2013 The base-N representations of 263 for N = 2, …, 9 are: 100000111 base 2 100202 base 3 10013 base 4 2023 base 5 1115 base 6 524 … Continue reading

## #math trivia #262 solution

#math trivia for #September19: #262 is a palindrome that’s twice a palindrome. Which other day-numbers (1-365) have this property? — Burt Kaliski Jr. (@modulomathy) September 20, 2013 We’re restricted to even palindromes, so our set of candidates (same forward and reverse) is: 2, 4, 6, 8 22, 44, 66, 88 202, 212, 222, 232, 242, … Continue reading

## #math trivia #261 solution

#math trivia for #September18: #261 = 29*9; September is the 9th month. Is day 29*M always in month M? What about other multiples of M? — Burt Kaliski Jr. (@modulomathy) September 19, 2013 Yes, day 29*M is always in month M: Day 29: January 29 Day 58: February 27 Day 87: March 28 Day 116: … Continue reading

## #math trivia #259 solution

#math trivia for #September16: #259 has two squares side by side. Do any day-numbers have two squares overlapping? — Burt Kaliski Jr. (@modulomathy) September 17, 2013 The side-by-side squares are of course 25 and 9. The problem doesn’t state exactly how much overlapping is allowed, so many forms are possible. Presumably, every digit is involved … Continue reading

## #math trivia #260 solution

#math trivia for #September17: #260 is number of license plates with letter then number. How many if both digits can be letter or number? — Burt Kaliski Jr. (@modulomathy) September 18, 2013 The count of 260 comes from the product of the number of letters, A-Z, which is 26, and the number a single-digit numbers, … Continue reading

## #math trivia #258 solution

#math trivia for #September15: #258 consists of three digits in an arithmetic progression. Which other numbers in the 200s do? — Burt Kaliski Jr. (@modulomathy) September 16, 2013 The digits 2, 5 and 8 form an arithmetic progression because each successive pair has the same difference: 5-2 = 8-5 = 3. The answers consist … Continue reading

## #math trivia #257 solution

#math trivia for #September14: #257 is a prime of the form 2^(2^n)+1. What is n? Which other day-numbers (1-365) have this form?— Burt Kaliski Jr. (@modulomathy) September 15, 2013 Answer: n = 3 gives 2^(2^n) + 1 = 2^(2^3) + 1 = 2^8 + 1 = 257. Other day-numbers of this form are 3 … Continue reading

## #math trivia #256 solution

#math trivia for #September13: #256 is the last 8th power <= 365. How many years of day-numbers does it take to get to the next 8th power? — Burt Kaliski Jr. (@modulomathy) September 14, 2013 The next 8th power is 38 = 6561. It takes almost 18 years of day-numbers (365 or 366 numbers per … Continue reading