Six people participated in a checker tournament.
Each participant played exactly three games with each of the other participants.
How many games were played in all?

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Solution

Finding the total number of games played:
The first player plays $3$ games with each of the other $5$ players.
Therefore, the total number of games he played $5 \times 3 = 15$
The second player plays $3$ games with $4$ others,
So, the total number of games he played $3 \times 4 = 12$
The third player plays $3$ games with $3$ others,
So, the total number of games he played $3 \times 3 = 9$
Similarly, fourth players played $3 \times 2 = 6$ games
And fifth player played $3 \times 1 = 3$ games
Thus, the total number of games played $15 + 12 + 9 + 6 + 3 = 45$

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Six people participated in a checker tournament. Each participant played exactly three games with each of the other participants. How many games were played in all?

Six people participated in a checker tournament.
Each participant played exactly three games with each of the other participants.
How many games were played in all?