Clara from the United World College Singapore wrote:
If I was doing 4 houses and 4 teddies, I would make 2 of the houses red and the other 2 houses blue. And the 4 teddies, 2 red and the other 2 blue. I would put 1 of the red teddies in the blue House, and put 1 of the blue teddies in the red house. Then I would put the other two teddies in the opposite house.
Tim has been very busy arranging teddies. He sent us pictures of his arrangements. Well done Tim!
Tim said that he couldn't arrange the houses and teddies on the map when there were six colours, but he wasn't sure why. In fact, this is quite a famous problem. You can read about it on the NRICH site or at www.cut-the-knot.org
, for example (our teddy bear problem is equivalent to finding two orthogonal Latin squares of different orders ).