#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 of days in the week divides into 231 = 234 – 3, so that there are 3 days left over. In addition to 7, the divisors of 231 are 1, 3, 11, 21, 33, 77, and of course 231. If a week were 1 or 3 days long, it wouldn’t make sense to speak of N weeks + 3 days (one would just round up to the next whole number of weeks). However, if a week were 11, 21, 33, 77 or 231 days long — all of which are longer than the assumed 7 — then it would be still be N weeks + 3 days.

Exercise for the reader: What’s the value of N for each of these cases?