4. You are given 20 boxes. 19 of the boxes each have 20 balls weighing 30kg per ball. However, one box has 20 balls weighing 29kg each. All the balls and boxes are identical in appearance. You are asked to determine which box contains the 29kg balls. You have a suitable scale, but may only take a single measurement. No other measurements may be taken (like trying to determine by hand). You may remove balls from the boxes but may still only take one measurement. How can you determine the box with 29kg balls.

Considering you can only weigh the balls extracted once and you need to find the box with balls that are 1-kilo lighter; here are the steps you can follow:

Number the boxes from 1 to 19.
Extract the same number of balls as the number given to the box. For example, from box 9 extract 9 balls.
Weight all the balls together.
Find out the box with the 29 kg balls. Here is an example:

The total weight using this method would be 6,300 kg which is the result of adding 30 kg (first box) + 60 kg (second box)... However, since there is a box with lighter balls the total weight will be less.

Let's imagine the weight is 6,290, this means there are 10 fewer kilos and therefore the box with the lighter balls is box 10 since this is the box number from which 10 balls were extracted.

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