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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, 3 months ago

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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:



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.

Alex Li - 2 years, 3 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.

Randy Yap - 2 years, 3 months ago

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You nailed it.Awesome!

Shiv Ram - 2 years, 3 months ago

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