Balance Lab: find a hidden weight using all the clues

Before you start

Use addition and subtraction up to 24. A, B and C are three objects, each with a different whole-number weight from 1 to 9. The unit is the same throughout. Paper counters can help.

Work through this example

A + B = 7, B + C = 9, and A + C = 8. Find A. Each letter keeps the same weight in every clue.

Reason step by step

1. Add the three totals: 7 + 9 + 8 = 24. Each object appears twice, so two copies of A + B + C weigh 24. One copy weighs 12.
2. Remove B + C, which weighs 9, from the total 12. A = 12 − 9 = 3. Similarly B = 12 − 8 = 4 and C = 12 − 7 = 5.
3. Check all clues: 3 + 4 = 7, 4 + 5 = 9, 3 + 5 = 8. The weights are different and within 1–9. Submit 3 when the target is A.

A mistake worth understanding

A = 2 and B = 5 fit the first clue. The second then gives C = 4, but A + C would be 6, not 8. Fitting one or two clues is not enough.

Try it yourself

New clues: A + B = 9, B + C = 11, A + C = 10. Find B and verify the other two weights.

Use the idea in the game

Start with the first difficulty in Balance Lab. Translate each shape into a letter. At higher difficulty, some clues contain two copies of a shape: count them before calculating. The “halve the total” shortcut only works when every object occurs exactly twice.

About & help

These examples were written for Piko Game. Generated game questions may differ. A score describes a game attempt, not mastery of a school curriculum.

Content and corrections

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