Equation Pyramids: Stuck? Call a brick x. Equation pyramids are built so that the 'call it x' move is the way in. 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
Each brick is the sum of the two bricks under it. Only a few bricks are given, and plain adding and taking away runs out.
A worked sample
Find what you can
The base brick 11 and the row-2 brick 15 above it: 15 − 11 = 4. That is as far as plain arithmetic goes: every other brick depends on two unknowns.
Call it x
Call the second base brick x. Then the brick above it and the 4 is x + 4, and the first base brick is 15 − x.
Write the bricks above
Row 1, left: 15 + (x + 4) = x + 19. Row 1, right: (x + 4) + 15 = x + 19. Both bricks are the same.
One equation
The top is 56, so (x + 19) + (x + 19) = 56, which is 2x + 38 = 56. Then 2x = 18 and x = 9.
Fill in the rest
With x = 9 everything follows: the first base brick is 15 − 9 = 6, the middle of row 2 is 9 + 4 = 13, and row 1 is 28 and 28. Check: 28 + 28 = 56.
Your turn
Try it: call it x
Some bricks are given. Call a base brick x, write the bricks above it, and solve. Type your numbers and press Check.
Why it is worth doing
Calling an unknown x is the first real step into algebra, and here the pyramid does the bookkeeping for you: every brick above is just x plus something.
How a page looks in the book
A low-resolution page from Math Pyramid Equation Puzzles: One Variable, so you can see the layout. Nothing on it is solved.
Books mentioned
Math Pyramid Equation Puzzles: One Variable
600 very hard pyramids in three sections of 4, 6 and 9 rows, with a technique page up front and full solutions. Puzzles in this book need the 'call it x' move.
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