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2024 InIMC keystage2-EMIC individual Question 11

xIMC · 2024 InIMC keystage2-EMIC individual

Question 11

The $4\times6$ rectangle is formed by using 3 pieces of $1\times1$ square tiles, 2 pieces of $2\times2$ square tiles, 1 piece of $2\times1$ rectangle tile, 4 pieces of $1\times2$ rectangle tiles and 1 piece of $3\times1$ rectangle tile as shown in the diagram below.

Question illustration

In how many different ways can we paint one or more pieces of tile so that the total area of the painted tile(s) is 4 units?

(Note: when painting a piece of tile(s) – all of its tiles must be fully painted.)