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Teddy Town

Stage: 1, 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Tim has been very busy arranging teddies. He sent us pictures of his arrangements. Well done Tim!

Red and yellow teddies and their housesRed, yellow and blue teddies and their housesRed, yellow and blue teddies and houses arranged on the mapRed, yellow, blue and green teddies and their housesRed, yellow, blue and green teddies and their houses arranged on the map Red, yellow, blue, green and purple teddies and their housesRed, yellow, blue, green and purple teddies with their houses arranged on the map
Red, yellow, blue, green, purple and black teddies and their houses

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 order 6).