The scale that holds only ten bolts

Question

A workshop has five boxes of bolts. Good bolts weigh exactly 20 grams. One box is full of bolts from a bad batch that each weigh 21 grams; every other box is good. You have a digital scale that shows an exact reading, but you may read it only once, and the scale's tray is small: it holds at most ten bolts. The usual trick is to take 1 bolt from box 1, 2 from box 2, and so on up to 5 from box 5. That needs 15 bolts, which do not fit. Find the bad box with a single reading.

Accepted Answer

Take 0 bolts from box 1, 1 from box 2, 2 from box 3, 3 from box 4 and 4 from box 5. That is exactly 10 bolts, which fits on the tray. Read the scale once. If all ten bolts were good they would weigh 200 grams. Each bad bolt adds 1 gram, so the excess above 200 grams tells you how many bad bolts are on the tray: - excess 4 grams: the bad bolts are the four from box 5 - excess 3: box 4 - excess 2: box 3 - excess 1: box 2 - excess 0: none of the bolts on the tray is bad, so the bad box must be the one you took nothing from, box 1 The idea. In the classic version you take a different positive num…

The scale that holds only ten bolts

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