Number Bank Pyramids: An empty pyramid and a bank of numbers. Each number is used exactly once. This is one of the many kinds of math pyramid we make, and here is how it works, with a video, a worked sample and a pyramid you can try right on this page.
The rule
Place every number from the bank exactly once so that each brick is the sum of the two bricks under it.
A worked sample
The top is the biggest
Every brick is a part of the top, so the top is the largest number in the bank: 21.
Split 21 into two bricks
The two bricks under the top must add to 21. In the bank, only 13 + 8 do. Which is on the left? The base brick 3 is given: if the left brick were 13, the brick beside 3 would be 10, which is not in the bank. So the left brick is 8 and the right one is 13.
Fill the base
8 − 3 = 5, and 13 − 5 = 8. The base is 3, 5, 8, and every bank number has been used once: 21, 13, 8, 8, 5, 3.
Your turn
Try it: spend the bank
Use each bank number once. The 3 is given. Type the numbers into the empty bricks, then press Check.
Why it is worth doing
There is no calculating from a given row here. You decide where a number can possibly go, and the bank tells you straight away when a guess is wrong.
How a page looks in the book
A low-resolution page from Number Bank Pyramids, so you can see the layout. Nothing on it is solved.
Books mentioned
Number Bank Pyramids
A whole book of bank puzzles, where the logic is placement rather than arithmetic. Hints and full solutions are in the back.
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More field notes
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The Case of the Vanishing Trophy: What It Can Do for Players
The Case of the Vanishing Trophy (Ages 8 to 12): what is in it, what players can get out of it and how to run it.
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Gauss's Trick: Add 1 to 100 in Ten Seconds
The famous 1 + 2 + 3 + ... + 100 shortcut, why it works (with drawings), what we really know about the story, and the pyramid of bricks hiding inside it.
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