You have four coins to sort with a standard balance scale. Their weights are 20g, 21g, 22g and 23g. Prove that there is no strategy which can guarantee sorting the coins with only three weighings.
The scale balance can produce only two results (left side heavier, right side heavier), with a single exception: if you weigh two coins against two coins, in just ONE case you get an "equal" result.
Thus, in three weighings, you might get, tops, 2x2x3=12 different results, but there are 4!=24 ways of ordering four coins, so that's not enough.
You need more weighings.