#math trivia for #September6: #249 follows this pattern: 49 is a 2nd power. What other three-digit numbers also have this pattern? — Burt Kaliski Jr. (@modulomathy) September 7, 2013 Every number is a first power of itself, so 100 through 199 all have the pattern. For the remaining powers: 2nd power — 2 followed by … Continue reading

## #math trivia #177 solution

#math trivia for #June25: #177 equals x^2 + 2^x for what integer x? — Burt Kaliski Jr. (@modulomathy) June 25, 2012 Answer: x = 7. One way to solve this is to note that the largest that x can be is 7, otherwise 2x would exceed 177. That also happens to be the answer.

## #math trivia #248 solution

#math trivia for #September5: #248 has three powers of the same number. What other three-digit numbers are similar? (Digits may repeat.) — Burt Kaliski Jr. (@modulomathy) September 6, 2013 In the current example, 2, 4 and 8 are all powers of 2. To see what the others might be, let’s start with the possible “bases” … Continue reading

## #math trivia #176 solution

#math trivia for #June25: #176 is a multiple of 11 but unlike 22, 33, 44, … doesn’t have repeated digits. Or does it? — Burt Kaliski Jr. (@modulomathy) June 24, 2012 Answer: 176 would have repeated digits in a redundant decimal representation, where each digit can have more values than the usual 0-9. In particular, … Continue reading

## #math trivia #247 solution

#math trivia for #September4: #247 is the difference of two squares and the product of two primes. What are they and how are they related? — Burt Kaliski Jr. (@modulomathy) September 5, 2013 Answer: The squares are 256 and 9; the primes are 13 and 19. The relationship is as follows: 256 is the square … Continue reading

## #math trivia #175 solution

#math trivia for #June23: #175 is 1200 base 5. In what other base(s) does it have a four-digit representation? — Burt Kaliski Jr. (@modulomathy) June 24, 2012 A four-digit representation base B covers numbers between B3 and B4-1. (As usual, it is assumed that the leading digit is at least 1.) Therefore, it’s sufficient to … Continue reading

## #math trivia #246 solution

#math trivia for #September3: #246 has an “even-digit-count” of 3. What even-digit-count occurs most often among day-numbers (1-365)? — Burt Kaliski Jr. (@modulomathy) September 4, 2013 Intuitively, I’d guess that the most frequent even-digit-count is probably 1, because that’s what it would be for two-digit numbers, as well as numbers in the 100-199 and 300-365 … Continue reading

## #math trivia #174 solution

#math trivia for #June22: #174 is yet another tri-composite (product of three distinct primes). What’s the next one? — Burt Kaliski Jr. (@modulomathy) June 23, 2012 Answer: The next tri-composite after 174 is 182, which is the product of the three distinct prime factors 2, 7 and 13. (I found this by trial and error, … Continue reading

## #math trivia #245 solution

#math trivia for #September2: #245 can be expressed as a^2+b^2+c^2 for positive integers a, b, c in three ways. What are they? — Burt Kaliski Jr. (@modulomathy) September 3, 2013 The three ways are 12+102+122 22+42+152 82+92+102 The third way is an interesting one because the integers are consecutive. If we let x denote the … Continue reading

## #math trivia #173 solution

#math trivia for #June21: #173 is a prime. What’s the largest prime you need to try to divide it by to know this? — Burt Kaliski Jr. (@modulomathy) June 22, 2012 An easy way to test whether a (small) number is prime is to see whether it’s divisible by any smaller primes. This is effectively … Continue reading