# Pentaminoes

*Material Required: Chart paper, pen.*

Pentaminoes are made by joining five squares so that at the joints, one side of a square fully joins with one side of another. There are twelve possible arrangements in which five squares can thus be joined to each other. Hence there are 12 possible pentaminoes.

Ask the students to find out all the possible pentaminoes. Let them cut out these pentaminoes from card paper. The total area of the pentaminoes, assuming each small square from which they are made up to be of unit area is 12 x 5 = 60 square units. Give the students a 8 x 8 board which contains 64 squares. Can the square board be covered with all the twelve pentaminoes, so that four squares remain. Although there are many possible ways of doing this, it may take a while to find even one arrangements which fills 60 of the 64 squares. Some of these possible arrangements leave four squares exactly in the middle. Can the students find such solutions?