## Entering The Iceberg

• The Size 1 Sphinx is made from six equilateral triangles.
• [The Size 1 Sphinx can also be made from several other shapes, but that's another story.]
• Four of the Size 1 Sphinxes make the Size 2 Sphinx.
• Since this new Sphinx demonstrates that four Sphinxes make a Sphinx, then four Size 2 Sphinxes will make another, larger Sphinx which will be Size 4.

Size 1

Size 2

PAUSE HERE, IF NECESSARY, TO PRINT MORE SPHINX SHAPES.

TRY THE SIZE 4 PROBLEM.

Of course it follows that four Size 4 Sphinxes will make a Size 8 and so on.

You might also imagine Size 1 being made from 4 smaller Sphinxes and each of those from 4 smaller Sphinxes and so on!

But now a mathematician might ask:

If we can make Sizes 1, 2, & 4, is it possible to make Size 3

- and if it is -

how many Sphinx shapes would be needed?

TRY THE SIZE 3 PROBLEM.

At this point you could return to the Iceberg of the Sphinx page and move on to the next link. However, without actually struggling with the problem yourself you will not appreciate the significant difference between the Size 4 problem and the Size 3 problem. You might expect Size 3 to be easier, but...