Weights

This is an old one, but I enjoyed when my dad showed it to me when I was just a wee lad:

You have 10 numbered boxes numbered 1 - 10 with steel balls inside and a scale.

Each box has the same amount of steel balls inside as the number on the box indicates.
All the balls have the same weight (10 units) except in one of the boxes all the balls weigh (9 units).

By only using the scale once, how can you determine in which box the lighter balls are?

I'm presuming these scales measure units, not that they're the balancing kind.

Stack all the boxes on the scales. If all boxes contained balls of 10 units the total would be (1+2+3+4+5+6+7+8+9+10)*10 units = 550 units.

The amount that the measured total differs from 550 equals the amount of balls that weigh 9 units not 10, and hence tells us the number of the box they're in.

Does that sound right? 😕

Originally posted by jot

I'm presuming these scales measure units, not that they're the balancing kind.

Stack all the boxes on the scales. If all boxes contained balls of 10 units the total would be (1+2+3+4+5+6+7+8+9+10)*10 units = 550 units.

The amount that the measured total differs from 550 equals the amount of balls that weigh 9 units not 10, and hence tells us the number of the box they're in.

Does that sound right? 😕

Originally posted by jot
Stack all the boxes on the scales. If all boxes contained balls of 10 units the total would be (1+2+3+4+5+6+7+8+9+10)*10 units = 550 units.
The amount that the measured total differs from 550 equals the amount of balls that weigh 9 units not 10, and hence tells us the number of the box they're in.