September Problems of the Month Posted on August 30th, 2019 by

Congratulations to last year’s top solvers: Filip Belik and James Wittrig!
Once again, we’ll be hosting “Problems of the Month” throughout the fall semester, and we invite everyone throughout the college to take part! Students, faculty, and staff are all welcome to submit solutions, and there are prizes for the top student solvers during the fall (details below).

Problems #1 and #2 this month are just a matter of arranging things nicely, and counting:

#1. Numbers which differ by less than three (like 4 and 6, or 10 and 11) are bitter enemies who can’t stand to be near each other. Numbers which differ by three or more are always good friends and rejoice in each other’s company. Fill in the circles with the numbers 1–10 so that every number is connected only to friends, never to enemies. Use each number once.

#2. How many different solutions are possible for problem #1? State the number of solutions clearly, and prove that your answer is correct.

Problem #3 is also about triangles, but it’s too hot to print on WordPress!

See the complete set of all three problems here: September 2019 Problems of the Month [PDF]

The fine print: Solutions are welcome from all Gustavus students, faculty and staff. Each month’s solvers will be announced along with a running scoreboard for the Fall Series. Prizes of $125 (first place) and $50 (runner up) will be awarded to the top student solvers at the end of the Fall Series; students who have solved at least three problems during the Fall Series are eligible for the prizes. To submit your solutions:

Email solutions to, or
Submit written solutions to Professor Siehler’s mailbox (by the door of Olin Hall 310).


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