With the Australian Open coming soon, the coach has some tennis puzzles to challenge the team.
Novak, Roger, and Rafa play an exhibition in which two play a set and the winner stays on court to play the waiting player. At the end of the event, Rafa has played 15 sets, Roger has played 14 sets, and Novak has played 9 sets.
What pair played in set number 13?
Maria will be playing a singles match, and to win the match, she must win two out of three sets. In tennis, a game is won by the first player to win four or more points by a margin of at least two. A set is won by the first player to win six or seven games by a margin of at least two. At six games apiece, a set is decided by a tiebreaker in which the first player to win seven or more points by a margin of at least two wins the set.
What is the longest streak of consecutive points possible for Maria to lose in a match and still win the match?
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Solutions to week 120
In Breakfast, Lunch, or Dinner?, Malcolm is finishing lunch. The proof required in The 2018 Puzzle can be stated as follows: Consider a plane containing any pair of the points and imagine the plane rotating in such a way that it always contains the two points. A line perpendicular to the plane will trace out a great circle on the celestial sphere. Produce such circles for every pair of points from the 2,018. Now pick a plane with fixed perpendicular that misses all the produced circles on the celestial sphere. This plane can be moved back and forth on the perpendicular and will cross only one point at a time among the 2,018. It can then be moved so that 1,009 are on each side of it.
Breakfast, Lunch, or Dinner? answer explained:
The minute hand is on a minute mark one minute ahead of the hour hand only when the hour hand is on the 11th minute mark and the minute hand is on the 12th minute mark. It follows that it is either 2:12 am or 2:12 pm. Since one doesn’t normally finish eating a meal at 2:12 am, Malcolm is finishing lunch.
Links to all of the puzzles and solutions are on the Complete Varsity Math page.
Come back next week for answers and more puzzles.