Tag Archives: problem solving

2022 William Lowell Putnam Math Competition

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Nineteen UML students spent six hours on December 3, 2022 competing in the 83rd annual William Lowell Putnam Mathematics Competition. Every year, thousands of students in the United States and Canada enter the competition. In each of two 3-hour sessions, they work on six difficult problems without the aide of any technology. One of the problems this year was

Let n be an integer greater than or equal to 2. Over all real polynomials p(x) of degree n, what is the largest possible number of negative coefficients of p(x)2?

Students working in the morning session.

Student solutions are graded by a committee of the Mathematical Association of America and results will be announce in a few months. They will appear on the Putnam Archive: https://kskedlaya.org/putnam-archive/. Professor Kenneth Levasseur supervised the competition at UML.

UML Participation in the 2018 William Lowell Putnam Math Competition

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2018 William Lowell Putnam Math Competition at UML

Forty-six UMass Lowell students participated in the 2018 William Lowell Putnam Mathematics Competition on Saturday, December 1. The competition, sponsored by the Mathematical Association of America, took place concurrently throughout the US and Canada. Last year, 4,638 students from 575 institutions participated. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. Here is one of them:

Find all ordered pairs (a,b) of positive integers for which 1/a + 1/b = 3/2018.

A complete list of problems:  putnam2018probs

Professor Kenneth Levasseur served as supervised competition at UML.   Thanks to the Honors College for providing refreshments for the students on the day of the event.

Results will be announced in late March.

2016 William Lowell Putnam Mathematics Competition

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Twenty-one UMass Lowell students competed in the 2016 William Lowell Putnam Mathematics Competition on Saturday, December 3. The competition took place concurrently throughout the US and Canada. Last year 4275 students students from 554 colleges and universities competed participated. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. The consensus of students at the end was that this problem was one of the easiest:

Suppose that S is a finite set of points in the plane such that the area of triangle ABC is at most 1 whenever A, B, and C  are in S. Show that there exists a triangle of area 4 that (together with its interior) covers the set S.

 

Thanks to the Honors College for providing refreshments for the students on the day of the event.

Results are normally announced in late March.

2015 William Lowell Putnam Mathematics Competition

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Twenty-four UMass Lowell students competed in the 2015 William Lowell Putnam Mathematics Competition on Saturday, December 5. The competition took place concurrently throughout the US and Canada. Normally, around 5,000 students compete each year. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. The consensus of students at the end was that this was the easiest.

Given a list of the positive integers 1, 2, 3, 4, …, take the first three numbers 1,2,3 and their sum 6 and cross all four numbers off the list. Repeat with the three smallest remaining numbers 4, 5, 7 and their sum 16. Continue in this way, crossing off the three smallest remaining numbers and their sum, and consider the sequence of sums produced: 6, 16, 27, 36,…. Prove or disprove that there is some number in this sequence whose base 10 representation ends with 2015.
Thanks to the Honors College for providing refreshments for the students on the day of the event.
Results are normally announced in late March.

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