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?

#LogicThinking #Analytic

Easy Math Editor

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Comments

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.

Alex Li - 5 years, 11 months ago

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 - 5 years, 11 months ago

You nailed it.Awesome!

Shiv Ram - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$