MathDB

You have a

7\times 7

board divided into

49

boxes. Mateo places a coin in a box.
a) Prove that Mateo can place the coin so that it is impossible for Emi to completely cover the

48

remaining squares, without gaps or overlaps, using

15

3\times1

rectangles and a cubit of three squares, like those in the figure. https://cdn.artofproblemsolving.com/attachments/6/9/a467439094376cd95c6dfe3e2ad3e16fe9f124.png b) Prove that no matter which square Mateo places the coin in, Emi will always be able to cover the 48 remaining squares using

14

3\times1

rectangles and two cubits of three squares.

Problem Statement