# How would this equation be solved by divide and conquer?

: A king has 32 golden coins, one of which he knows is counterfeit. The counterfeit gold

coin weighs less than a regular coin. You have been assigned to use a balance (scale) to

determine which one of the coins is not pure gold. Explain how you would accomplish

this using the scale a minimum number of times (find a divide & conquer approach for

your solution). How many times did you use the scale?

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Divide them into two groups of 16.

Put one group on each side of the scale.

The lighter group contains the counterfeit.

Now take these 16 coins and divide into two groups of 8

Put one group on each side of the scale.

The lighter group contains the counterfeit.

Now take these 8 coins and divide into two groups of 4

Put one group on each side of the scale.

The lighter group contains the counterfeit.

Now take these 4 coins and divide into two groups of 2

Put one group on each side of the scale.

The lighter group contains the counterfeit.

Now take these 2 coins and divide into two groups of 1

Put one group on each side of the scale.

The lighter group contains the counterfeit.