### Brain Teasers

# Chess Tournament II

The first chess tournament ended. Bab, Beb, Bib, Bob and Bub became good friends, and returned to their houses.

They told their wives about the tournament. Their wives were also chess players, and they decided to hold another tournament.

This time, each of the 10 players was going to play against each other player once, with an exception that no games were played between the couples. So a total of 40 games would be played.

After some days passed, they decided to have a get-together. Bub asked the other people how many matches until then they had played.

Something fun was that Bub heard 9 different answers.

How many matches until then had Mrs. Bub played?

They told their wives about the tournament. Their wives were also chess players, and they decided to hold another tournament.

This time, each of the 10 players was going to play against each other player once, with an exception that no games were played between the couples. So a total of 40 games would be played.

After some days passed, they decided to have a get-together. Bub asked the other people how many matches until then they had played.

Something fun was that Bub heard 9 different answers.

How many matches until then had Mrs. Bub played?

### Hint

If you can't figure it out, draw a diagram.### Answer

Each player could play at most 8 matches, so the answers Bub heard was 0, 1, 2, 3, 4, 5, 6, 7, 8 in some order.Assume without loss of generality that it was Bab that had played 8 matches. Then all players except Mrs. Bab must have played against Bab, and it must have been Mrs. Bab who had played no matches.

Then, assume without loss of generality that Beb had played 7 matches, and then all players except Mrs. Bab and Mrs. Beb must have played against Beb, and it must have been Mrs. Beb who had played 1 match.

Repeat this and we know that Mrs. Bub had played 4 matches.

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