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Difficulty: MediumPuzzle Details:

A farmer was asked how many chickens he had sold at market that day. His reply was:

"I've had four customers today, and each bought half of my remaining chickens, plus a half chicken."

The farmer sold all of his chickens at market that day. How many chickens did the farmer sell?

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[Ref: ZVAK] © Kevin Stone 

Answer: 15 chickens.

The first customer bought  15 ÷ 2 + ½ = 8 (leaving 7)
The second customer bought  7 ÷ 2 + ½ = 4 (leaving 3)
The first customer bought   3 ÷ 2 + ½ = 2 (leaving 1)
The first customer bought   1 ÷ 2 + ½ = 1

The answer can be worked out in the following way:

The fourth customer can only have bought one chicken, otherwise there would be some chickens left. The third customer bought all but 1, so total - (total ÷ 2 + ½) = 1. This can be solved algebraically or it's easy to see that the total must have been 3. This method keeps working until we reach the first customer.



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