Problem of the Week 938

Lions and Lambs

Suppose some lions and lambs satisfy:

  1. There are at least two lions.
  2. Each lion has bitten at least three lambs.
  3. For any two lions, there is exactly one lamb that has been bitten by both.
  4. For any two lambs, there is at least one lion that has bitten both.
  5. One of the lions has bitten six lambs.

How many lions are there? How many lambs are there?

Source: Andy Liu, Univ. of Alberta
© Copyright 2001 Stan Wagon. Reproduced with permission.

13 Sept 2001