HHC 2014 Programming Contest

[David Hayden]

An odd number of PDPs happen in pairs when 12/31 and 1/1 are prime, but only when the next New Year isn't also prime. Assume there is a 4 year range. Call the number representing the year before this range X. Now compute the offsets K1, K2, etc. to the supposedly prime days. Take the offsets mod 3 and you find that at least one is 0, 1, or 2. That means that regardless of what X mod 3 is, (X + Kn) mod 3 will be zero for at least one of the Kn's.