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A round-robin tournament with 10 people.

  • Find the maximum possible points for second place
  • Find the minimum possible points for second place
  • Find the maximum possible points for second last place
  • Find the minimum possible points for second last place

Came across this question on Glassdoor on a company-specific page

My approach:

Each team plays with 9 other teams (round-robin) hence 9 matches. 1st place would have 9 points in the best case/maximum possible.

Hence maximum possible for 2nd place = 8

Not sure how to approach the other parts

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Minimum possible points for second place:

Assume the 1st place team wins every match. Then each team has eight other teams they might beat. Assuming they each won half of these, they'd each score 4 points, and this is possible - imagine arranging the teams in a circle, you can let each team beat the four teams clockwise from them.

Second-last place:

Is just a mirror of second place, flipping 'won' to 'lost'. So minimum is (9 - 8 =) 1 and maximum is (9 - 4 =) 5.

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