Royal Arm Wrestling
How many arm-wrestles will there be in the royal arm wrestling championship?
Age
11 to 14
Challenge level
Problem
The Kings of Clubs, Diamonds, Hearts and Spades, and their respective Queens, are having an arm wrestling competition. Everyone must wrestle everyone else, except that no King will wrestle his own Queen. How many wrestling bouts are there?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
24
The 8 individuals will each wrestle 6 others. This suggests that the number of bouts is 8 x 6 = 48. However, each bout has been counted twice in this calculation, so the number of bouts is 48/2 = 24.
The 8 individuals will each wrestle 6 others. This suggests that the number of bouts is 8 x 6 = 48. However, each bout has been counted twice in this calculation, so the number of bouts is 48/2 = 24.