TOT 2006 Fall - Senior A-Level p6 deck of 52 cards divisible by 13!
Source:
February 25, 2020
number theorycombinatorics
Problem Statement
Let us say that a deck of cards is arranged in a “regular” way if the ace of spades is on the very top of the deck and any two adjacent cards are either of the same value or of the same suit (top and bottom cards regarded adjacent as well). Prove that the number of ways to arrange a deck in regular way is
a) divisible by (3)
b) divisible by (5)