Shape Value Logic Puzzles Practice Test Worksheets
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.
For students who can solve equations, but lose marks when the unknowns are hidden inside shape-value puzzles.
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What Do Shape Value Questions Look Like?
Students are given a grid of shapes where each shape represents a specific number, along with row and column totals. They must use arithmetic clues and logical deduction to find the numerical value of an unknown shape. Here is a worked example.
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.
Rules to Help You Solve Shape Value Questions
As shown in the example above, visual algebra puzzles follow consistent mathematical logic. 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.
Two More Worked Examples
Practise finding shapes when two unknown copies appear together, then learn how to select efficient starting clues from a full three-by-three grid.
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.
Choose a Useful Row and Column
Question: Work out the value of the Triangle. Each row adds to the total on its right, and each column adds to the total below it.
Worked Method
Step 1: Scan for three matching shapes. The bottom row contains three circles with a total of 18, so Circle = 18 ÷ 3 = 6.
Step 2: Find a clue containing a triangle and only known shapes. The rightmost column contains Circle + Triangle + Circle and has a total of 23.
Step 3: Substitute Circle = 6: 6 + Triangle + 6 = 23. Therefore Triangle = 23 − 12 = 11.
Tip: You do not need to find the square first. Choose the row or column that uses values you already know, and read the total at the end of that same row or column.
