(a) In a round-robin tennis tournament with n players, every tennis player plays
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Question
(a) In a round-robin tennis tournament with n players, every tennis player plays against every other player. Let T(n) be the total number of tennis matches taking place among the n players. Find a recurrence for T(n) and explain in words why T(n) satisfies this recurrence. (b) In a board game, players must place colored tiles in a single row. There are red 1 times 1 tiles, yellow 2 times 1 tiles, blue 2 tiles 1 tiles, purple 3 times 1 tiles, and green 3 times 1 tiles. Let C(n) be the number of different n times 1 colored rows that can be created using these tiles. Find a recurrence for C(n) and explain in words why C(n) satisfies this recurrence.Explanation / Answer
1(a)
Let T(n) be the number of matches for n players
We know that each player will play with every other player , So n-1 for base case
If there are less than 2 players than , T(n) = 0
If there are 2 players than , T(2) = 1
Therefore,
T(n) = T(n-1) + n-1 for n>2
2 for n=2
and 0 otherwise
If we solve the recurrance we get. T(n) = nC2
=> n(n-1)/2
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