Problem of the Month
You and I are going to play a game; to play, we'll need 12 coins, and a copy of the diagram pictured above. Here's how the game works:
We will take turns placing coins on the lettered spaces in the diagram. You must always place exactly one coin on your turn, and you must always place it on an empty space. Whoever goes first may place their first coin on any space; thereafter, you must place your coin on a space connected to where the last coin was placed. The first player to have no legal moves, loses.
For example: if I go first, I might place a coin on space A. You would then have to place a coin on a space connected to A: either B, D, E, F, or J. Perhaps you choose space E. Then I would have to place a coin on space F or K (not space A, since there is already a coin there). Perhaps I choose space K. Then perhaps you choose space D, and I choose space J. You would then be stuck; all the spaces connected to space J (A, D, and K) already have coins on them. So I'd win.
I'm giving you the option of going first or second. Which should you choose? And what strategy would you follow to win?
Send your answers to this problem to me (Joseph DiMuro) at email@example.com by September 30, 2014.
“I would choose math at Biola is that math is taught as a part of God's creation and my love for math grows alongside my love for God.”
Applied Mathematics Major
“Being a math major has equipped me with deeper knowledge, understanding, and fascination of the subject. Due to this, I feel more excited, confident, and prepared to help future math students succeed in this subject.”
Secondary Teaching Mathematics Major
“I'm so glad I chose to study math at Biola - the faculty incredible and invested in their student’s lives, and I know they care about me in and out of the classroom. It's also been an invaluable opportunity to have consistent integration of my major and my faith and see how God can be glorified through math, which has been one of my favorite aspects of the department.”
Pure Mathematics Major
Why Choose Mathematics at Biola?
- Thorough in both educational quality and personal attention to students
- Faculty and students work together to make the study of mathematics a successful and enjoyable learning experience
- Involvement in the Putnam Exam; a nationwide contest for math students
- Experienced faculty who not only teach classes in which they are specialists, but work on research projects with individual students
- Small class sizes
- Readily accessible computing facilities