Number Pyramid Puzzles Practice Test Worksheets
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.
For students who understand addition, but need practice working up, down, and across a number pyramid without guessing.
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What Do Number Pyramid Puzzles Questions Look Like?
Number pyramid puzzles require you to fill in missing blocks by using the rule that each block is the sum of the two directly beneath it. Solving them involves alternating between addition and subtraction. Here is a worked example.
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.
Answer: A (3)
Check: 6 + 3 = 9, matching the block above the final pair.
Tip: Do not jump straight to n. First find the adjacent bottom-row value and the block directly above the pair.
Rules to Help You Solve Number Pyramid Puzzles Questions
To solve number pyramid puzzles like the example above, identify connected trios of blocks to find missing values. Keep these key rules in mind:
🔺 Rule 1: Add upwards
Add the two adjacent blocks directly beneath a block to find its value.
Example from the diagram: 10 and 5 are the two adjacent blocks directly beneath 15: 10 + 5 = 15.
↘️ Rule 2: Subtract downwards
If a block and one of the two blocks directly beneath it are known, subtract the known lower value from the upper value to find the other lower value.
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: In Example 1, 22 - 12 = 10 reveals a bottom-row value. Then 10 + 5 = 15 reveals the block directly above that pair.
✅ Rule 4: Check the final path
The final value of n should still make every neighbouring block agree with the pyramid rule.
Example: In Example 1, n = 3 sits beside 6 below a block worth 9. Check: 6 + 3 = 9.
Two More Worked Examples
Here are two more examples showing how to work from the right and avoid treating rows as isolated sums.
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.
Answer: D (5)
Check: 5 + 11 = 16, matching the block above the first pair.
Tip: The best starting point is not always near n. Start where the pyramid gives you a complete subtraction.
Do Not Treat the Rows as Separate Sums
Question: Find n in the bottom-left block. Use the given clues to work through the adjacent pairs.
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.
Answer: B (11)
Check: 11 + 5 = 16, matching the block above the first pair.
Tip: Add the two adjacent blocks directly beneath each upper block. Adding an entire row is not the rule.
