Sphinx Album ... Page 4

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What Happens If...?

The fascination of the Sphinx seems to be in the way it replicates itself - 4 Sphinxes make a Sphinx is the starting point. Are there other shapes which behave this way? Certainly.

• 4 Size 1 Squares make a Size 2 Square.
• 4 Size 2 Squares make a Size 4 Square.
• 4 Size 4 Squares make a Size 8 Square.
• And now we are growing just like the Sphinx does.
• But what about Size 3 Squares? If one existed, how many Size 1 Squares might be needed to make it? Could it be made? Certainly. We have all made a 3x3 square of 9 squares in the past. But this is the same reasoning which opened the door to the Sphinx problem.

John has donated some work from an old notebook which might start you off on the hunt.

Click the image to enlarge.
For best printing save the enlarged form and import into a word processor.

Follow this link to Task Centre Home page.