Notes from an Inspector's Notebook: April 2005

At the BCME 6 conference in Britain last month I caught up with John Hibbs (retired - but still very active - HMI) who discovered one of the original Size 3 Sphinx solutions. He had rediscovered the drawing of his solution, so, as an item of history a scan of it has been added to the record of his solution at:
http://www.blackdouglas.com.au/project/sphinx/sfnx3sol.htm

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.

Somehow though growing squares seems a bit common place. Are there still other shapes with this property?

John has donated some work from an old notebook which might start you off on the hunt. Since this work can be seen as a What happens if...? question developing from the Sphinx problem, it has been recorded on Page 4 of the Sphinx Album.

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