Number Pyramid Puzzles
Number pyramid puzzles ask you to fill a missing value by working through connected sums. Each block depends on the two blocks below it, so the strongest solutions use addition and subtraction in a careful order.
The Rules Every Number Pyramid Question Uses
Every puzzle uses the same structure: a number in a block is made from the two blocks directly beneath it. The challenge is choosing whether to build upwards or undo the sum by subtracting.
🔺 Rule 1: Add upwards
If two touching lower blocks are known, add them to find the block above.
Example from the diagram: 10 and 5 are touching lower blocks, so the block above is 15.
↘️ Rule 2: Subtract downwards
If a top block and one lower block are known, subtract to find the missing lower block.
Example from the diagram: 22 is above 12 and a blank, so the blank is 10.
🧭 Rule 3: Follow the chain
One new value often unlocks the next row. Keep moving through connected blocks, not random gaps.
Example: Once the blank is 10, it can help make the next connected block above.
✅ Rule 4: Check the final path
The final value of n should still make every neighbouring block agree with the pyramid rule.
Example: If a lower block is filled in, re-check that it adds correctly with the block next to it.
How to Solve Number Pyramid Puzzles
Three useful moves: build upwards when you can, subtract downwards when you must, and avoid treating the pyramid as separate rows.
1. Build a Missing Bottom Value from the Left
Question: Find n in this number pyramid.
Worked Method
Step 1: Work down from 22: 22 - 12 = 10.
Step 2: Build upwards: 10 + 5 = 15, and 22 + 15 = 37.
Step 3: Continue the chain: 63 - 37 = 26, then 26 - 15 = 11.
Step 4: Finish on the right: 11 - 5 = 6, 20 - 11 = 9, so n = 9 - 6 = 3.
Tip: Do not jump straight to n. First find the values that touch it.
2. Work from the Right When That Side Is Given
Question: The right-hand side gives 10 and 13. Find n on the bottom left.
Worked Method
Step 1: Start on the right: 13 - 10 = 3.
Step 2: Build and subtract through the middle: 3 + 3 = 6, 6 + 13 = 19, and 39 - 19 = 20.
Step 3: Move left: 20 - 6 = 14, then 14 - 3 = 11.
Step 4: Use the left side: 30 - 14 = 16, so n = 16 - 11 = 5.
Tip: The best starting point is not always near n. Start where the pyramid gives you a complete subtraction.
3. Do Not Treat the Rows as Separate Sums
Question: Find n when the bottom row includes 11, 5, 8, 2, and 7.
Worked Method
Step 1: Use the connected right side first: 9 - 7 = 2.
Step 2: Build upwards from there: 8 + 2 = 10, and 10 + 9 = 19.
Step 3: Subtract back through the middle: 42 - 19 = 23, 23 - 10 = 13, and 13 - 8 = 5.
Step 4: Now use the left side: 29 - 13 = 16, so n = 16 - 5 = 11.
The trap: The pyramid rule only applies to touching blocks. Adding across a whole row gives the wrong path.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Number Pyramid pack contains 90 puzzles across 3 printable test sets. Each set includes structured pyramid questions plus step-by-step answers.
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