A nursery-style mobile hangs from the ceiling, perfectly level. Two of its weights are marked, two are a mystery, and one of those mysteries is today’s question. No algebra degree needed, just careful counting.
The puzzle
- The top bar hangs from its pivot (the gold dot). Its left arm is 2 notches long and its right arm is 3 notches long. A smaller bar hangs from each end.
- The left bar holds a block weighing 8 one notch left of its pivot, and a block weighing 4 two notches right of it.
- The right bar holds a circle one notch left of its pivot, and a triangle three notches right of it. Neither weight is marked.
- Every bar hangs perfectly level, the notches on each bar are evenly spaced, and the bars and strings weigh nothing.
What does the triangle weigh?
Show hint
A bar balances when weight times distance from the pivot is the same on both sides, just like a seesaw. Work out what the whole left side weighs first, then move up to the top bar.
Show answer
Answer: the triangle weighs 2 (and the circle weighs 6).
Step by step:
- Left bar. 8 × 1 = 8 and 4 × 2 = 8, so it balances. Everything hanging there weighs 8 + 4 = 12.
- Top bar. The left side pulls 12 × 2 notches = 24. To balance, the right side must pull 24 too, and it hangs 3 notches out, so everything on the right bar weighs 24 ÷ 3 = 8.
- Right bar. The circle sits 1 notch out and the triangle 3 notches out, so the circle must be 3 times as heavy as the triangle. Together they weigh 8.
- Three triangles’ worth plus one triangle makes four triangles’ worth = 8, so the triangle weighs 2 and the circle weighs 6. Check: 6 × 1 = 2 × 3. ✓
The trick is that the right bar alone can’t tell you the answer; it only fixes the ratio. You need the top bar to learn the total.