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<p>But you’re assuming that the real coin’s weight “x” is an integer, which you never stated in the original problem. And even if “x” were an integer, your method doesn’t work, because you’d need to balance up to (40 choose 20)/2 times to see whether a set of 20 coins balances the other 20 coins.</p>
<p>I’d stick to inhaven’s reasoning, which is valid and can be proved algebraically.</p>