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Common Answers

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Puzzle - Answer

4 shepherds were watching over their flocks and they were commenting on how many sheep they each had. If Alan had three more sheep, then he'd have one less sheep than Brian. Whereas Dave has the same number as the other three shepherds put together. If Charles had three less sheep, he'd have exactly treble the number of Alan. If they were evenly distributed they'd each have eleven sheep. How man sheep does Alan have?

 [Ref: ZIZG] © Kevin Stone

Answer: 3.

If we denote Alan by A, Brian by B, Charles by C and Dave by D we can find the answer in the following way. Since A + B + C = D and A + B + C + D = 44, it is easy to see that D has 22 sheep. So A + B + C = 22. We can use this along with the two other facts, A + 3 = B - 1 and C - 3 = 3A, to find that A has 3, B has 7, C has 12 and D has 22. In a little more detail:

A + B + C = 22 (1)
A + 3 = B - 1 (2)
C - 3 = 3A (3)

Rearrange (3) to give C = 3A + 3 and replace the C in (1) to give A + B + 3A + 3 = 22. Simplified this gives B = 19 - 4A (4). Rearrange (2) to give B - A = 4. Use (4) in the place of B to give 19 - 4A - A = 4 to give A = 3. Now use A to work out B, and then C. QED.

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