# Brain Teasers and Puzzles

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## Puzzle Details

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

If Alex had three more sheep, then they'd have one less sheep than Blake.

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

If Charlie had three less sheep, they'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?

If we denote Alex by A, Blake 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.