MathDB

15

Part of 2019 Hanoi Open Mathematics Competitions

Problems(1)

HANOI letters in a 2x5 rectangle (HOMC 2019 JI-15)

Source:

11/7/2020
Given a 2×52\times 5 rectangle is divided into unit squares as figure below. https://cdn.artofproblemsolving.com/attachments/6/a/9432bbf40f6d89ee1cbb507e1a3f65326c6a13.png How many ways are there to write the letters H,A,N,O,IH, A, N, O, I into all of the unit squares, such that two neighbor squares (the squares with a common side) do not contain the same letters? (Each unit square is filled by only one letter and each letter may be used several times or not used as well.)
combinatorics