# Be the Detective!

You have 10 boxes of balls (each ball weighing exactly 5 grams) with one box full of defective balls (each of the defective balls weigh 4 grams). You are given an electronic weighing machine and only one chance at it. How will you find out which box has the defective balls?

Note by Shiv Ram
2 years, 12 months ago

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## Comments

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Take one ball from the first box, two from the second, and so on, until $$10$$ from the last. Suppose that the total mass is $$n$$ grams, and that there are $$x$$ balls with mass $$4$$ grams and $$y$$ balls with mass $$5$$ grams. You then have the following system of equations:

$$x+y=55$$

$$4x+5y=n$$.

This system of equations always has a unique solution, which means that, because you took a different number of balls from each box, you can definitively determine which box contains the defective balls.

- 2 years, 12 months ago

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Like what @Alex Li said, if your total, n, comes out to 274 grams, then you know from deduction that box 1 contains the defective ball. Likewise, if n turns out to be 270 g, then the culprits must be in box 5 ( the missing 5 grams comes from the 5 defective balls of 4 g each) and so forth.

- 2 years, 12 months ago

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You nailed it.Awesome!

- 2 years, 12 months ago

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