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Prove that all 101 balls have the same weight

(This is more of an extended comment rather than a full answer.) As far as I can see, the notion of parity is crucial for this puzzle to work. This can be seen by generalizing a bit: Instead of 101 ...
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Prove that all 101 balls have the same weight

If you are teaching young people, I would probably start with a much smaller example that almost works. Imagine you have balls weighing 1, 2, 3, 4, and 5lbs. In total they weigh 15 lb. If I remove the ...
• 5,830
Accepted

Balls of different weights: how few balls can there be?

Well, at first look, either all numbers must be even or all must be odd. If this is not the case, some partial sums will be even and some odd, and no partial sum may be odd (since we have to ...
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1 vote

Balls of different weights: how few balls can there be?

It's possible with and here's why: This is optimal: It is also optimal in terms of W...
• 147k
1 vote

Prove that all 101 balls have the same weight

Maybe it would be helpful to look at the answer as a system of equations? Consider a scaled-down problem with only 5 total balls. Call the balls' weights $a$, $b$, $c$, $d$, and $e$. Assume the balls ...
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