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Square Bisection

Age 11 to 14 Short Challenge Level:

Any line which passes though the centre of the square divides the square into two congruent shapes. An example is shown below.

Figure 1

There are an infinite number of suitable lines (lines passing through the centre, at any angle) so there are infinitely many ways the square can be cut in half with a single straight cut.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.