December Problems of the Month

Posted on December 2nd, 2019 by

Congratulations to November’s solvers: Filip Belik, Mike Hvidsten, and Ha Le. November’s problems seems to have been particularly challenging!
On to December: Problem #1 is a little arithmetic curiosity:

The four-digit numbers 3025 and 2025 have an unusual property: (30+25)^2 = 3025 and (20+25)^2 = 2025. That is, if you put a plus sign in the middle of the number, and square the sum, you get the original four-digit number back. Can you find a ten-digit number with the same property? Here’s a frustrating near-miss: (11110+22222)^2 = 1111022224, not the desired 1111022222. Can you do better?

Problem #2 asks you to work out the angles on the graphs of a couple of your favorite trigonometric functions, and Problem #3 is about letters, randomly-chosen words, and the power of proof and deductive reasoning over chaos. Or something like that. Read the complete set of three problems in full detail here: December 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. Faculty and staff will earn the admiration of the community and further burnish the already gleaming reputation of our dear alma mater. To submit your solutions:

Email solutions to jsiehler@gustavus.edu, or
Submit written solutions to Professor Siehler’s mailbox (Olin Hall 310) by December 20th, 2019.

 

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