Skip to content
One Quick Try

Shape Equation Puzzle

Each shape stands for a number. Work them out from the clues, then answer the last line.

Type
Logic
Takes
about 2-4 min
Result in
correct

Shape Equations

~2-4 min

  1. Each shape stands for a whole number.
  2. Work the numbers out from the clues, then answer the last line.
  3. 6 puzzles, getting harder. × comes before + and −, as usual.

Each clue adds only one new shape, so take them in order.

Your result: — / 6

How it's measured

Try another challenge

  • Make 24

    Use all four numbers to make 24.~2-4 min

  • Matrix Reasoning

    Find the picture that completes the grid.~3-5 min

  • Digit Span

    Repeat the digits, forward or backward.~2-4 min

  • Water Jug

    Measure an exact amount with unmarked jugs.~1-4 min

  • River Crossing

    Get everyone across the river safely.~2-5 min

  • Tower of Hanoi

    Move every disk in the fewest moves.~1-5 min

How do shape equation puzzles work?

Each shape stands for a whole number, the same number every time it appears. The first lines are clues, such as three triangles making 15, so one triangle is 5. Use what each clue tells you in the next one, then work out the last line, where the answer is a question mark. In this version every shape is a whole number from 1 to 10, and no two shapes in a puzzle are equal.

How this puzzle works

There are 6 puzzles, from simple sums to ones with multiplication and subtraction. Type your answer and press Enter. Whether you are right or not, the value of every shape is shown before the next puzzle, so you can check your working. The clock runs over the whole set.

How do you solve shape math puzzles?

Take the clues in order. Each clue here brings in exactly one new shape, so it can always be solved with what you already know: if two squares plus a 5 make 19, the squares make 14 and one square is 7. These puzzles are small systems of equations, and working through them one unknown at a time is called substitution.

Every puzzle has exactly one answer. The site's tests generate a hundred of each kind and try every possible value for each new shape, to prove that only the right one fits.

Why do people get these puzzles wrong?

Mostly order of operations. Multiplication comes before addition and subtraction, so 2 + 3 × 4 is 14, not 20. The page says so whenever a × appears. The versions shared online also often hide tricks, such as a picture that changes slightly between lines or counts as half. There are no tricks here: a shape is always the same shape and the same number.

How is your result calculated?

Your result is how many of the 6 puzzles you answered correctly, with the total time from the first puzzle to your last answer. You also see how many of the two hardest you got right.

This is a recreational puzzle, not a maths assessment. For a number puzzle with only four numbers, try Make 24; for rules in pictures instead of numbers, the Matrix Reasoning Test.

Questions

Do I multiply before adding?
Yes, as in ordinary arithmetic: × comes before + and −. So triangle + square × circle means multiply the square and the circle first, then add the triangle.
Can a shape stand for zero or a fraction?
No. In this version every shape is a whole number from 1 to 10, and every answer is a whole number too.
Is there always exactly one answer?
Yes. Each clue adds only one new shape, so its value is fixed by the clues before it. The site's tests check this for every kind of puzzle.
What are these puzzles called?
Shape math, shape equation or fruit puzzles, after the versions shared on social media with fruit instead of shapes. In maths terms they are small systems of equations.
Are there trick questions?
No. A shape always means the same number, nothing is hidden, and the order of operations is stated on screen when it matters.