Four shepherds were watching over their flocks, and they were commenting on how many sheep they each had.

If Alex had three more sheep, then he'd have one fewer sheep than Billie.

Whereas Drew has the same number as the other three shepherds put together.

If Charlie had three fewer sheep, he'd have exactly three times the number of Alex.

If they were evenly distributed, they'd each have eleven sheep.

How many sheep does Alex have?

Puzzle Copyright © Kevin Stone

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Hint

Find how many sheep Drew has first.

Answer

3.

Reasoning

If we denote Alex by A, Billie by B, Charlie by C, and Drew by D and number the clues.

If Alex had three more sheep, then he'd have one fewer sheep than Billie.
Whereas Drew has the same number as the other three shepherds put together.
If Charlie had three fewer sheep, he'd have exactly three times the number of Alex.
If they were evenly distributed, they'd each have eleven sheep.

By (4):

A + B + C + D = 44

And, by (2), these are shared equally between A + B + C and D.

So D = 22, and A + B + C = 22 (*****)

By (1):

A + 3 = B – 1

A + 4 = **B**

By (3):

C – 3 = 3A

**C** = 3A + 3

Substitute **B** and **C** in (*****):

A + (A+4) + (3A+3) = 22

5A + 7 = 22

5A = 15

A = 3

And, B = 7, C = 12.

Double-Checking

A = 3, B = 7, C = 12, D = 22.

(1) 3 + 3 = 7 – 1

(2) 3 + 7 + 12 = 22

(3) 12 – 3 = 3 x 3

(4) 3 + 7 + 12 + 22 = 44, and 44 ÷ 4 = 11 each.

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