18. Snow White organised a chess competition for the seven dwarves, in which each dwarf played one game with every other dwarf. On Monday, Grumpy played 1 game, Sneezy played 2, Sleepy 3, Bashful 4, Happy 5 and Doc played 6 games. How many games did Dopey play on Monday?
A 1
B 2
C 3
D 4
E 5
Solution
C

All the following arguments refer to the games played on Monday. Doc played 6 games and so played all the other dwarves. Therefore, Grumpy's game was against Doc. Similarly, since Happy played 5 games and didn't play against Grumpy and Sneezy only played two, Sneezy's games were against Happy and Doc. Bashful played 4 games and didn't play against Grumpy or Sneezy and Sleepy only played three games and so Sleepy's games were against Doc, Happy and Bashful. Therefore Dopey played against Doc, Happy and Bashful so played 3 games.