## #math trivia #April3 solution

Burt Kaliski Jr. (@modulomathy)
4/3/12 7:34 AM
#math trivia for #April3: day*month = year today. How many other days does this happen in ’12? Is there any year with more “product” days?

This problem, unlike most (but like the next one) is about the actual date, not the day-number (which would be #94).

The other days this year where day*month = 12 are January 12, February 6, March 4, June 2, and December 1. There are thus six “product” days in 2012.

Is it possible to have more? If we want to include January in the pattern, the two-digit year must be 31 or less. The only numbers in that range with more suitable divisors than 12 is 24, with seven divisors between 1 and 12. If we want to get more divisors, we could look for a number larger than 31 that’s also divisible by 5 and 10. For example, 60 has eight divisors between 1 and 12 (it gains 5 and 10 but loses 8). However, 60 is too large not only for January but also for February, so there would be only six “product” days. Other years fall short for similar reasons. The only year with more “product” days is thus ’24.