Problem of the Month
Let's play a game. We have a few piles of pennies: one pile has 3 pennies, one has 6, one has 10, and one has 12.
We'll take turns removing pennies. On your turn, you may take as many pennies as you want from any single pile. The twist: if you take just one penny from a pile, your opponent MUST take pennies from that same pile on his next turn. The first player to have no legal moves, loses.
For example: I could take 5 pennies from the third pile, leaving 3-6-5-12. Then you might take 1 penny from the fourth pile, leaving 3-6-5-11. I would then be forced to take from the fourth pile; maybe I take 2 pennies, leaving 3-6-5-9. And so on.
Starting from 3-6-10-12, would you want to go first or second? You don't need to give me the complete winning strategy; just say whether you want to go first or second, and why.
Send your answers to this puzzle to me (Joseph DiMuro) at email@example.com by April 30, 2015.
“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