Here’s a curious puzzle, a classic.

Take a pile of nine pebbles and split them into piles. Say, piles of 4 and 5. On the side, write 5 x 4 = 20 . Now split the pile of 5 into two, say piles of 2 and 3. Write 2 x 3= 6 . Keep doing this—splitting piles and recording products—until you have nine piles each of 1 pebble.

Now sum up the products. You are sure to get the magic sum of 36.

Try it! Make different splitting choices along the way. The magic sum of 36 is inescapable!

[What if you start with different initial pile sizes. What are some other magic numbers?]

This is only the beginning of the story!

Freaky Fractions!

Crazy 1s!

And More!

Here’s an essay explaining the mathematics and ways for you to create you own crazy, mind-blowing pile-splitting puzzles.

Pile Splitting

And Yet Even More!

Young high-school student Elizabeth Gerber took matters even further. Why split only into two piles at a time? Why not play with something even wilder, like matrices? She did!

Elizabeth’s Pile Splitting with Matrices

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