Imagine 101 coins in front of you. All of them look the same, but it is known that among them there is a defect one, a coin that doesn't have the same mass as his friends. What is the smallest number of measurements on scales without weights that should be carried out in order to determine whether the coin has a higher or lower weight than others?
2026-04-13 11:59:06.1776081546
Invalid Coin measuring?
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1
$2$? Weigh $33$ coins against another $33$.
Case I. they match. Then the odd one is one of the missing $35$ (and we have $66$ normals). So just weigh $35$ normals against the rest.
Case II. they don't match. Then the other $35$ are all normal. So weigh the lighter $33$ against $33$ normals. If they match then the odd coin is heavy. If they don't match the odd coin is light.