# Posted in August 2013 …

## #math trivia #169 solution

#math trivia for #June17: #169 is one of eight day-numbers that are squares of primes. What are the others? — Burt Kaliski Jr. (@modulomathy) June 18, 2012 Recall that “day-numbers” are integers between 1 and 366 — the numbers of the days of the year (366 is included because the problem was given during a … Continue reading

## #math trivia #240 solution

#math trivia for #August28: #240 is highly composite: it has more divisors than any smaller number. How many? What was the previous record? — Burt Kaliski Jr. (@modulomathy) August 29, 2013 The number 240 has 20 divisors:  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, … Continue reading

## #math trivia #168 solution

#math trivia for #June16: #168 is 2^3 * 3^1 * 7^1. How many positive divisors does it have? — Burt Kaliski Jr. (@modulomathy) June 16, 2012 The number of positive divisors of 168 is 16. Given the factorization of 168, we know that any positive divisor must have the form 2i * 3j * 7k … Continue reading

## #math trivia #239 solution

#math trivia for #August27: #239 is 0xef in hexadecimal. In what other bases would it have two digits in increasing consecutive order? — Burt Kaliski Jr. (@modulomathy) August 28, 2013 For clarity, we’ll assume that “two digits in increasing consecutive order” means that, like 0xef, there are exactly two digits in the representation of the … Continue reading

## #math trivia #167 solution

#math trivia for #June15: #167 is x*(x+2)-1 for what value of x? — Burt Kaliski Jr. (@modulomathy) June 16, 2012 This one is fairly straightforward:  If we want x*(x+2)-1 = 167, then we need x and (x+2) to be factors of 168.  Given that 168 = 12*14, it follows that x is 12. We should … Continue reading

## #math trivia #238 solution

#math trivia for #August26: #238 has the form abc where a^b = c. Which other three-digit numbers have this form? (Some may not be obvious.) — Burt Kaliski Jr. (@modulomathy) August 27, 2013 The other numbers are: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191 201, 212, 224 (next would be the current 238) 301, 313, 329 401, 414 … Continue reading

## #math trivia #237 solution

#math trivia for #August25: More counting: #237 has the form abc where b^2 = a+c. How many three-digit numbers are like this? — Burt Kaliski Jr. (@modulomathy) August 26, 2013 Answer:  16.  Similar to the solution to #236, there are at least two ways to count: By a‘s, seeing how many c‘s yield a value … Continue reading

## #math trivia #236 solution

#math trivia for #August24: #236 has the form abc where a*b = c. How many three-digit numbers are like this? — Burt Kaliski Jr. (@modulomathy) August 24, 2013 The answer is 32. There are two main ways to figure it out. Assume that a is between 1 and 9 in the following, i.e., leading 0s … Continue reading

## #math trivia #235 solution

#math trivia for #August23: Four substrings of #235 are prime: 2, 3, 5, 23. Find a three-digit number where all six substrings are prime. — Burt Kaliski Jr. (@modulomathy) August 24, 2013 Let abc be a three-digit number.  If all six substrings of abc are prime, then we must have: a, b, c are prime … Continue reading

## #math trivia #234 solution

#math trivia for #August22: #234 is 33 weeks + 3 days, assuming a 7-day week. If weeks were longer, could it still be N weeks + 3 days? — Burt Kaliski Jr. (@modulomathy) August 23, 2013 The answer is yes:  234 days could still be N weeks + 3 days as long as the number … Continue reading