MathDB

Tracy has been baking a rectangular cake whose surface is dissected by grid lines in square fields. The number of rows is

2^n

and the number of columns is 2^{n \plus{} 1} where

n \geq 1, n \in \mathbb{N}.

Now she covers the fields with strawberries such that each row has at least 2n \plus{} 2 of them. Show that there four pairwise distinct strawberries

A,B,C

and

D

which satisfy those three conditions: (a) Strawberries

A

and

B

lie in the same row and

A

further left than

B.

Similarly

D

lies in the same row as

C

but further left. (b) Strawberries

B

and

C

lie in the same column. (c) Strawberries

A

lies further up and further left than

D.

Problem Statement