MathDB

5

Part of 1999 Finnish National High School Mathematics Competition

Problems(1)

Generalized domino tiles

Source: Finnish Mathematics Competition 1999, Final Round, Problem 5

11/14/2011
An ordinary domino tile can be identifi ed as a pair (k,m)(k,m) where numbers kk and mm can get values 0,1,2,3,4,50, 1, 2, 3, 4, 5 and 6.6. Pairs (k,m)(k,m) and (m,k)(m, k) determine the same tile. In particular, the pair (k,k)(k, k) determines one tile. We say that two domino tiles match, if they have a common component. Generalized n-domino tiles mm and kk can get values 0,1,...,n.0, 1,... , n. What is the probability that two randomly chosen nn-domino tiles match?
probabilitycombinatorics unsolvedcombinatorics