How to play Balance Scales
Every set of scales balances — work out the whole-number weight of each shape. Also known as Shape weight puzzles.
The rules
- Each set of scales balances: both pans weigh the same.
- The same shape always has the same weight.
- Numbers on a pan are weights in kilograms.
- Every shape weighs a whole number from 1 to 9, and the answer is unique.
Playing Balance Scales on Puzzle Solvers
- Choose a level — from two shapes to five — and press New Puzzle.
- Every set of scales balances. The number on a pan is a weight in kilograms.
- Tap a shape in the answer row and type its weight. Every weight is a whole number from 1 to 9.
- Hint points at the scales that tell you a weight next — and explains why.
A worked example
Scale 1: two hearts balance 10 kg, so a heart weighs 5 kg.
Scale 2: a heart and a star balance 12 kg. With the heart worth 5, the star is 12 − 5 = 7 kg.
Strategies
- One unknown first. Find scales with only one kind of shape. Divide the weight by the number of shapes.
- Substitute. Once a shape is known, replace it by its weight on every other scale.
- Compare scales. If one scale has the same shapes as another plus one extra, the extra shape weighs the difference.
- Take away from both pans. The same shape on both pans can be removed without changing the balance.
Common mistakes
- Forgetting that a shape counted twice weighs twice as much.
- Guessing a weight before checking it against every scale.
Where it comes from
Balance puzzles have been used for generations to teach the idea of an equation. This version was made for this site.
Frequently asked questions
Can two different shapes weigh the same?
Yes — different shapes can have equal weights; only the same shape must always match.
Do I need algebra?
No — every step can be done by looking at the scales, though it is the same thinking.
Is there always one answer?
Yes — every puzzle is checked so that only one set of weights balances every scale.
Keep going
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All guides: How to play every puzzle and game.