Tukatoome Tiles

In her will to her favorite niece,

Aunt Tuka left a valuable piece.

But the piece, a tile with a unique design,

Was mixed with some others with similar lines.

So the niece had to follow the words of the will,

That told of the tile and how it was filled

With shapes of differing numbers and angles.

A problem the neice had to untangle.

Is the real tile X, Y, or Z?

The will will tell as you can see.

So take your time; think for a while.

Then find the real Tukatoome Tile.

To my niece:

My tile has polygons, more than meet the eye.

They fit together like a piece of pie.

Some are hidden and hard to see,

So, be sure to count them carefully.

The tile is worth 60 million they say,

And its value was found in the following way.

Three million for a triangle; for a quadrilateral four,

Five million for a pentagon; for a hexagon, one more.

Good luck,

Aunt Tuka

Reference from Greenes, Carol, Linda Schulman, Rika Spungin, Suzanne Chapin, Carol Findell. Mathletics: Gold Metal Problems. Providence RI: Janson Publications Inc., 1990. p. 1.