Ink-Blot Pyramids: Every brick is printed, but ink has covered some of the digits. 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. An ink blot hides exactly one digit, and no number starts with 0.
A worked sample
Start with the last digits
Look at the top two bricks: 4■ + 47 = ■2. The last digits must add up to a number ending in 2. Something plus 7 ends in 2, so the something is 5. The blot is a 5 and the left brick is 45. Now 45 + 47 = 92.
Take away
Next row down: ■4 + 23 = 47. Take away: 47 − 23 = 24. The blot is a 2.
One more take-away
2■ + 24 = 45. Take away again: 45 − 24 = 21. The blot is a 1.
Down to the base
1■ + 8 = 23, so 23 − 8 = 15, and the blot is a 5. The last blot: ■2 + 9 = 21, so 21 − 9 = 12 and the blot is a 1. Check: 9 + 15 = 24. It all fits.
Your turn
Try it: clear the ink
Type the hidden digit into each box, then press Check. Start with the last digits of the top row, as above.
Why it is worth doing
Ink-blot puzzles train a skill that plain sums do not: working out which digit can be there, using last digits, carrying and size. It is a good habit for checking any calculation.
How a page looks in the book
A low-resolution page from Ink-Blot Pyramids, so you can see the layout. Nothing on it is solved.
Books mentioned
Ink-Blot Pyramids
A whole book of ink-blot pyramids, 120 puzzles from easy to expert, for ages 10 to adult. Hints and full solutions are in the back.
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