Balance: a logic puzzle made of scales
Balance is a logic puzzle without numbers. A few scales are already set and tell you how shapes compare. Every shape has a fixed weight — nobody knows which. The question is not what could be true, but what must be true.
Free in the browser, without an account, in three difficulties.
The rules
- Every shape has a fixed weight. The same shape weighs the same everywhere — including when it sits twice on the same pan.
- All weights are greater than zero. That sounds like a formality and is a tool: it is why two shapes together are heavier than either of them alone.
- The scales are fixed. You weigh nothing and move nothing — they are the information you get.
- Correct means true in every case. A statement that holds for some weights and not for others is not the answer.
- “Not determinable” is an answer like any other — and the right one in roughly every fourth puzzle.
Strategy: three things that matter
- Do not count the symbols. Four shapes can be lighter than two; how many sit on a pan says nothing about weight. Every puzzle contains at least one scale where exactly that is the case.
- Cross out whatever sits on both sides. The same shape left and right changes nothing about the comparison. It is the first move and often the only one.
- Measure the difference, not the side. When two scales balance and differ in one shape, the difference has to come back somewhere else — and that tells you which way.
Four examples, step by step
The first three are the moves everything else is built from. The fourth is the real subject: sometimes nothing follows, and recognising that is the heart of the game. Under each example stands what the server's checker says — not what is claimed here.
This is what a puzzle looks like — a real one, straight from the generator. Which of the four answers must be true?
Answer:is heavier than
Example 1Cancelling — The same shape sits on both sides. It changes nothing about the comparison — take it off both pans and what remains is exactly the question.
Question:?Answer:is heavier than
Example 2Substituting — The second scale says two shapes weigh the same, so they may be swapped. Doing that turns the first scale into one that again carries the same shape on both sides — and that cancels.
Question:?Answer:is heavier than
Example 3Nothing weighs nothing — Every weight is greater than zero. A side made of two shapes is therefore heavier than either of them alone, and because the scale is balanced, that carries over.
Question:?Answer:is heavier than
Example 4Not determinable — The left side is heavier as a whole. That says nothing about a single shape: the lead may come from one or from the other. Two sets of weights satisfy the same scale and disagree on exactly this question — and where two answers are possible, neither is forced.
Question:?Answer:not determinable
Both sets of weights fit:5132and1642
Play it yourself
Balance in practice mode — one type, one difficulty, as often as you like, and none of it counts. If the shapes look familiar: they are the same six as in code deduction.