Bunuel wrote:
In a league of 8 teams, each team played every other team 10 times. The number of wins of the 8 teams formed an arithmetic sequence. What is the least possible number of games won by the champion?
A. 41
B. 42
C. 43
D. 44
E. 45
If every team plays exactly 1 match with every other team exactly once then Total Matches \(= \frac{8*7}{2} = 28\)
i.e Total matches if every team plays 10 matches with every other team = 28*10 = 280
Total Wins = 280
For them to be in arithmetic progression of 8 terms, Mean = median \(= 280/8 = 35\)
For mean/median of 8 terms in Arithmetic progression to be 35, the terms can NOT be consecutive so they must for an Arithmetic progression of even terms with median 35i.e. Numbers of wins will be {28, 30, 32, 34, 36, 38, 40, 42}Answer: Option B
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