MathDB

Combinatorics on a times b board

Source: Serbia MO 2018 P5

April 2, 2018

combinatorics

Problem Statement

Let

a,b>1

be odd positive integers. A board with

a

rows and

b

columns without fields

(2,1),(a-2,b)

and

(a,b)

is tiled with

2\times 2

squares and

2\times 1

dominoes (that can be rotated). Prove that the number of dominoes is at least

\frac{3}{2}(a+b)-6.