Three heavy and three light among six
Six coins, A to F, look identical. Exactly three are heavy and three are light; all the heavy ones weigh the same, and all the light ones weigh the same. You have a two-pan balance.
Show that two weighings are not enough to identify the three heavy coins, and give a procedure that always does it in three.
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There are 20 ways to choose which three coins are heavy, and two weighings have only 9 outcomes. For the procedure, weigh single coins against each other: a tilt tells you both coins' types at once.
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