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IMSO 2023 — Mathematics Exploration Question 3

IMSO Maths · IMSO 2023 — Mathematics Exploration

Question 3

A $5\times7$ board is to be partitioned into $1\times1$, $2\times2$ and $3\times3$ sub-boards. What is the smallest number of $1\times1$ sub-boards? Sketch one possible diagram. (2 marks)

Now use an $11\times11$ board under the same conditions. What is the smallest number of $1\times1$ sub-boards? Sketch one possible diagram. (4 marks)

**Correct answers with incorrect drawings will be given 0 marks.**