# PUTNAM 2022 QUESTIONS DETAILED WITH PROPER QUESTIONS FROM THE LATEST QUESTIONS PAPER 2022

The Putnam competition takes place on the first Saturday in December and consists of two three-hour sittings separated by a lunch break. The competition is supervised by faculty members at the participating schools. Each one consists of twelve challenging problems. The problems cover a range of advanced material in undergraduate mathematics, including concepts from group theory, set theory, graph theory, lattice theory, and number theory.

Each of the twelve questions is worth 10 points, and the most frequent scores above zero are 10 points for a complete solution, 9 points for a nearly complete solution, and 1 point for the beginnings of a solution. In earlier years, the twelve questions were worth one point each, with no partial credit given. The competition is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually zero or one point out of 120 possible, and there have been only five perfect scores as of 2021. In 2003, of the 3,615 students competing, 1,024 (28%) scored 10 or more points, and 42 points were sufficient to make the top percentile.

At a participating college, any student who wishes to take part in the competition may (limited by the number of spots a school receives); but until 2019 the school's official team consisted of three individuals whom it designated in advance. Until 2019, a team's score was the sum of the ranks of its three team members, with the lowest cumulative rank winning. It was entirely possible, even commonplace at some institutions, for the eventual results to show that the "wrong" team was picked, that some students not on the official team outscored an official team member.

For example, in 2010, MIT had two of the top five scorers in the competition and seven of the top 24, while Caltech had just one student in the top five and only four in the top 24; yet Caltech took first place among teams while MIT took second. In 2019 the rules of the competition changed, with a school's team consisting of its top three scorers, and the team ranks determined by comparing the sums of the scores of the team members.

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