# 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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Start out by balancing 6 coins on each side of the balance. If the balance shows the two sides equal, the coin you did not weigh is the odd one.

If one side is heavier, take those 6 coins and balance them 3 on a side.

One side should be heavier than the other.

Take the 3 coins from the lighter side, then select two of the 3, and balance them. If these two coins are the same, then the coin you did not select is the counterfeit. Otherwise, the lighter coin will show up in this step.