MathDB

Blocks in a 10 X 10 table

Source: International Zhautykov Olympiad 2013 - D2 - P3

January 17, 2013

rectanglecombinatoricsExtremal combinatoricscoveringSquaressquare grid

Problem Statement

10 \times 10

table consists of

100

unit cells. A block is a

2 \times 2

square consisting of

4

unit cells of the table. A set

C

n

blocks covers the table (i.e. each cell of the table is covered by some block of

C

) but no

n -1

blocks of

C

cover the table. Find the largest possible value of

n