For the riddle, see Balance puzzle

Balance puzzle

A number of logic puzzles exist that are based on the balancing of similar-looking items, often coins, to determine which one is of a different value within a limited number of uses of the balance scales...

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A balance puzzle is a mathematical puzzle

Mathematical puzzle

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules as do multiplayer games, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions....

 which challenges the solver to distribute a subset of numbers so that the several sides of a stylized diagram representing a balance scale are equal. The balance puzzle is a classical number puzzle in the World Puzzle Championship

World Puzzle Championship

The World Puzzle Championship is an annual international puzzle competition run by the World Puzzle Federation. The first one was held in New York in 1992...

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It consists in a mobile or tree structure, with designated positions where the player must hang specified weights, so that everything balances.
See examples below.

There are usually 8 to 12 consecutive numbers (weights) to place, which makes it much smaller than, for example, sudoku

Sudoku

is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid contains all of the digits from 1 to 9...

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As in many mathematical puzzles, the solution is unique.
Expert puzzlers often prefer puzzles where the rules explicitly states that there is only one solution.
This property allows for some reasoning strategies.
It also makes generating puzzles a bit more difficult.

Variants

• Balloon balance: same puzzle but with negatives weights also to be placed. example