Teddy Town - Part Three
There are sixteen teddies in Teddy Town - four red, four blue, four yellow and four green. There are also sixteen houses, four of each colour. Can you put them on the map of Teddy Town according to the rules?
Problem
This is part three of Teddy Town. Take a look at the main problem page for more information about what's happening here!
Getting Started
You could use counters or pieces of coloured card if you don't have teddies.
Have you checked your combinations are all different?
Student Solutions
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).
Teachers' Resources
Why do this problem?
Possible approach
Key questions
Possible support
Some children might find it easier to work out all the possible combinations of houses and teddies before putting them onto the grid - others might prefer to put all of the houses onto the grid first and then put the teddies on afterwards. If pupils are finding it difficult to check their solutions, they might benefit from using a checking mechanism for the first grid:
Possible extension