# Puzzle ZIZG

??

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 treble the number of Alex.

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

How many sheep does Alex have?

3.

Reasoning
If we denote Alex by A, Billie by B, Charlie by C, and Drew 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.

Note: BrainBashers has a Dark Mode setting.