[OK] We use cookies to personalise content and adverts. We also share information about your use of our site with our advertising partners who may combine it with other information you’ve provided to them or they’ve collected from your use of their services. You also agree to our terms and conditions (T&C).

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?

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.

Back to the puzzles...

Our Favourite Illusions

 Shadow Illusion What Am I? Hidden Faces Impossible Waterfall? Same Eyes? Impossible Prongs?
 Duck Or Rabbit? Spinning Dancer Who Turned To? Blind Spot The Butterfly Parallel Cafe Wall Lines?