# DECISION TREES. Suppose you have a set of 13 coins, one of which is counterfeit (lighter).?

Suppose you have a set of 13 coins, one of which is counterfeit (lighter). Draw a tree to show how you can figure out the counterfeit coin using an unlabelled balance using the fewest number of comparisons.

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Divide coins into two groups of 6 and set one aside. Put each group of 6 on a side of the scale. If they balance then the coin you set aside is counterfeit. If they are unbalanced, set aside all the coins in the heavier group and the originally set-aside 13th coin. Divide the remaining 6 coins into two groups of 3. Put each group of 3 onto opposite sides of the scale. Set aside all the coins in the heavier group. Divide the remaining 3 coins. Set one aside and put each of the remaining 2 on opposite side of the scale. If they are balanced, the set-aside coin is counterfeit, otherwise the counterfeit is the lighter of the coins remaining on the scale.

Minimum of 1 comparison, maximum of 3.