MathDB

N is a multiple of 3^{25}, but not a multiple of 3^{26}

Source: New Zealand NZMOC Camp Selection Problems 2018 p7

September 19, 2021

Coloringcombinatorial geometrycombinatorics

Problem Statement

Let

N

be the number of ways to colour each cell in a

2 \times 50

rectangle either red or blue such that each

2 \times 2

block contains at least one blue cell. Show that

N

is a multiple of

3^{25}

, but not a multiple of

3^{26}