Question 23. Snow White organized a chess competition for the seven dwarves in which each dwarf played one game with each of the other dwarves. On Monday, Grumpy played one game, Sneezy played two, Sleepy three, Bashful four, Happy five, and Doc played six games. How many games did Dopey play on Monday? Start off by listing out the seven dwarves and how many games each of them played on Monday. We do not know how many games Dopey played. However, we can start off with Doc. We know that Doc played six games and since there are seven dwarves, that means he would have had to play against each other dwarf one time. That would conclude his six games. With this, we also know that Grumpy played only one game, so his single game was against Doc. So we can no longer look at Grumpy and Doc. Next, we can look at Happy. Happy played five games total. There are four other dwarves for him to play against, so that works out since he played his one game already and these would be the next four. Sneezy, Sleepy, Bashful, and Dopey all Sneezy as well played two games, so we can also eliminate him. Next, we are left with Sleepy, Bashful, and Dopey who have each played two games so far. Since Bashful played four games, he's played two. He needs to play two more. They will be against Sleepy and Dopey. This way, we can get rid of Bashful as they've played their four games. Sleepy has played his three games and that leaves no one left to play games against Dopey, which means we can total up the three games that he played. So Dopey played C, three games on Monday.

chess competition

seven dwarves

Snow White

Dopey games

Monday games