You have added a row of a pyramid and you are not sure. Adding it all again is slow. There is a faster test that takes about five seconds, and it only needs to know whether a number is odd or even.
Three facts
Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9. Only the last digit matters, so 4,827 is odd however big it looks.
Using it on a pyramid
Here is a pyramid someone has filled in. One brick in the middle row is wrong. We will find it using only odd and even.
One brick may be off
The bottom row is 4, 7 and 3. The middle row says 11 and 9, and the top says 21.
Check the left brick
4 is even and 7 is odd. Even plus odd is odd, and 11 is odd. That fits.
Check the right brick
7 and 3 are both odd. Odd plus odd is even. But the brick says 9, which is odd. It cannot be right. (7 + 3 = 10.)
We found the mistake without adding anything. The check does not tell you the right number, only that this brick is wrong. For the right number, add it up: 7 + 3 = 10.
The limits of the check
The check catches a mistake only when the wrong answer has the wrong odd-or-even. If you are 2 out, or 10 out, the number is still the right kind, and the check says nothing. So a pass means probably fine and a fail means definitely wrong. It is a quick filter, not a proof.
Where else it helps
- Missing bricks. If the top is odd and one bottom brick is missing, work out the odd or even you need before you try numbers.
- Wrong-brick hunts. One brick in the wall is false. Run the check along each row to find the pair that disagrees.
- Everyday sums. 37 + 48 cannot end in an even number. It must be odd. 85 is, so you are on track.
Books mentioned
Find the Wrong Brick
130 mistake-hunt puzzles for teens and adults: one brick in each pyramid is wrong, and you find it. The whole book is this one kind of puzzle.
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Escape the Pyramid, Level 1
A math escape book with 45 locked chambers. Number pyramids and wrong-brick hunts are two of its 5 puzzle kinds, so the book is not all pyramids.
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