Sometimes a brick is missing and there is no way to add up to it. Both bricks next to it are unknown, or they only touch it from above. Then you do what mathematicians do. You give the missing number a name, usually x, and keep going. That is algebra, and it is gentler than it sounds.
The puzzle
A three-row pyramid. The top is 33. The bottom row is 5, a missing brick and 8. Find the missing brick.
What we know
Top 33, bottom left 5, bottom right 8. The middle of the bottom row is missing. Call it x.
Write the middle row using x
The left middle brick is 5 + x. The right middle brick is x + 8. We don't know their values yet, but we know how they are made.
Write the top using x
The top is the two middle bricks added: (5 + x) + (x + 8) = 13 + 2x. And the top is 33. So 13 + 2x = 33.
Solve for x
Take 13 away from both sides: 2x = 20. Halve both sides: x = 10.
Check by climbing
5 + 10 = 15 and 10 + 8 = 18. Then 15 + 18 = 33, the top we were given. It works.
The four steps, any time
- Name it. Call the missing brick x.
- Build upwards. Write each brick above as a sum, with x in it.
- Match the top. The top is a known number, so you get an equation.
- Undo. Do the opposite of each step on both sides until x stands alone. Then climb the pyramid to check.
Why this is worth learning
The same four steps solve equations in school: name the unknown, write what you know, undo it step by step. A pyramid is a friendly place to practise because you can check the answer yourself by climbing, so you never have to ask whether you are right.
Books mentioned
Math Pyramid Equation Puzzles: One Variable
600 very hard number pyramid puzzles with one variable, 4 to 9 rows, with full solutions. The puzzle in this post is a gentle first step; the book climbs far higher.
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A Puzzle a Day: 365 Equation Pyramids
A 'Call It x' puzzle a day for a year, with full solutions. The idea in this post is exactly what the book trains.
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