October Problems of the Month

Posted on October 1st, 2019 by

Congratulations to September’s supremely successful solvers: Filip Belik, Luke Haddorff, Tom LoFaro, James Wittrig, and Katherine Williams.

October’s Problem #1 is just a game of Xs and Os:

Imagine that the following list of three 7-letter words is made from tiles with X on one side, and O on the other side:
 

  1. OOOXXXX
  2. XXOXOOX
  3. OXXXXOO

Any one of the words can be changed to any of the others by flipping exactly four tiles (from X to O or vice versa). Your problem: Make a list of eight 7-letter words using Xs and Os, with the same property, that is, any word in your list can be changed to any other word in your list by flipping exactly four tiles.

Problem #2 is a “Let’s Make a Deal” – style challenge, and Problem #3 is a sweet little story about prime numbers which will warm your heart even as the days get colder (particularly if you solve it).

See the complete set of all three problems here: October 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 jsiehler@gustavus.edu, or
Submit written solutions to Professor Siehler’s mailbox (Olin Hall 310) by October 27th, 2019.

Happy solving!

 

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