Shape Value Logic Puzzles
Shape value questions are visual algebra puzzles. Each shape stands for a number, and the row and column totals give you the clues. This page shows how to work through them carefully and avoid common traps.
The Rules Every Shape Value Question Uses
The puzzles look different from ordinary equations, but they use the same ideas every time. Find a clean starting row or column, then use that value to unlock the next clue.
🔁 Rule 1: Same shape, same value
A circle has one fixed value throughout the whole grid. The same is true for every square and triangle.
Example: If Circle = 4, then three circles add to 12 anywhere in the puzzle.
🧩 Rule 2: Start with three matching shapes
A row or column with three identical shapes is usually the fastest first step. Divide the total by 3.
Example: Square + Square + Square = 6, so Square = 2.
➖ Rule 3: Substitute, then subtract
Once you know one shape, put its value into another row or column and subtract to find the missing shape.
Example: 2 + 2 + Circle = 7, so Circle = 3.
✌️ Rule 4: Watch for two of the unknown
Some clues leave two copies of the shape you want. Subtract the known value first, then halve what is left.
Example: Triangle + 11 + Triangle = 37, so 2 triangles = 26 and Triangle = 13.
How to Solve Shape Value Puzzles
One straightforward, one multi-step, and one classic mistake to avoid.
1. Starting with a Matching Row
Question: Square + Square + Square = 6. In the same grid, Square + Square + Circle = 7. Work out the value of the Circle.
Worked Method
Step 1: Three squares make 6, so one square is 6 ÷ 3 = 2.
Step 2: Substitute Square = 2 into the second clue: 2 + 2 + Circle = 7.
Step 3: 7 - 4 = 3, so Circle = 3.
Tip: A row with three identical shapes is often the cleanest place to begin.
2. Finding Two Copies of a Shape
Question: Circle + Circle + Circle = 33. Another clue says Triangle + Circle + Triangle = 37. Work out the value of the Triangle.
Worked Method
Step 1: Circle + Circle + Circle = 33, so Circle = 33 ÷ 3 = 11.
Step 2: Substitute Circle = 11 into the second clue: Triangle + 11 + Triangle = 37.
Step 3: Subtract 11 from 37 to get 26. That is two triangles, so 26 ÷ 2 = 13.
Tip: When the unknown appears twice, remember to divide the remaining total by 2.
3. Using the Wrong Total
Question: Circle + Circle + Circle = 18. A column total says Circle + Triangle + Circle = 23. Work out the value of the Triangle.
not just one circle
Worked Method
Step 1: Circle = 18 ÷ 3 = 6.
Step 2: Substitute carefully into the column: 6 + Triangle + 6 = 23.
Step 3: The two known circles add to 12. Then 23 - 12 = 11, so Triangle = 11.
The trap: Do not subtract just one circle. This clue contains two circles, so both known values must come off the total.
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 Shape Value Logic Puzzles pack contains 90 questions across 3 printable test sets. Each puzzle uses row and column totals to build mental arithmetic, logical reasoning, and early algebra confidence.
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