Each of 5 men played a game of chess with each of 5 women, and then each woman played a game of chess with each of the other women. How many games of chess were played? a) 20 b) 25 c) 35 d) 45 e) 50 Difficulty: Hard HINT First find the number of games played between the men and the women. Then find the number of games played between women. The sum of these two numbers is the total number of games played.

C: 35 Explanation: Each man will play 1 game of chess with each of the 5 women. Therefore, each man will play 5 games. Since there are 5 men, a total of 25 games will be played between the men and the women. Each woman will play 1 game of chess with each of 4 other women. In counting the number of games played, it is important to avoid counting any game more than once. The first woman will play 4 games. The second woman has already played the first woman, so she will play 3 additional games with the other women. Similarly, there are 2 more games played by the third woman, and 1 more game played by the fourth woman. All the games played by the fifth woman have already been counted. So the 5 women play a total of 4 + 3 + 2 + 1, or 10 games with each other. Thus, a total of 35 games of chess have been played.