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York Region District School Board

February 2023 - Problem of the Month

This Month’s Problem

Consider the following pattern.

The diagram contains 3 stages. In the first stage there is a square in the centre, surrounded by congruent squares on all sides. In the second stage, there is a square in the middle and on each side there are two attached congruent squares. In the third stage, there is a square in the middle and on each side there are three attached congruent squares.

How many squares will there be in stage 7?

 

Solution 

There will be 29 squares in stage 7.  How many will there be in stage 100?

 

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