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Upstate New York Math Team
Mathematical Problem Solving
Dear Upstate New York Math Team,
We had a surprise presentation yesterday from Mason Eyler, last year’s A Team captain of our ARML team. Mason shared 5 simple game theory type problems that led to fascinating results. Click on the button to download Mason’s problems, Zoom Whiteboard, and Answers (including a full solution for Problem 5).
Don’t read the answers until you’ve thought about the problems!
Some Game Theory Problems (36KB PDF)
Game Theory Answers (80KB PDF)
Here’s a topic list from Mason’s presentation. (Unfortunately, Zeitz’s textbook is not a good reference for any of these.)
Game Theory
Probability
Geometric Probability
Expected Value
Simon's Favorite Factoring Trick
The Fencepost problem aka OBOB "off-by-one bug"
We left off considering problem 5, a simple version of poker. To see Mason’s solution, click on the button above.
5) Alice and Bob are playing a simplified game of poker, where the deck contains three cards: 1, 2, and 3 (Queen, King, and Ace). Each player puts one dollar in the middle, before being dealt a random card without replacement. Each player looks at their own card, but not their opponents. Alice has the choice to bet (put another dollar in the middle) or check (do nothing). If she checks, both players reveal the cards and whoever has the higher card wins the two dollars in the middle. If she bets, Bob can either call or fold. If he folds, Alice wins automatically. If he calls, he puts in another dollar, and whoever has the higher card wins all four dollars in the middle.
What is each player’s optimal strategy, and what is the expected value of playing the game?
Thank you, Mason!
CUBRMC Problem Review: A few weeks ago we reviewed some of the 2024 Cornell University Big Red Math Competition problems. You can view our video recording here (Passcode: B7C*0q7C). The official contest problems and solutions are also available.
CUBRMC Official Problems and Solutions
We’re taking a short break until early December. Have a great Thanksgiving - get plenty of rest, eat well, spend time with your family, and try to solve Mason’s problem #5!
Japheth
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Japheth Wood is a coach for the Upstate New York Math Team and also a math professor at Bard College in Annandale-on-Hudson, NY.
*For our purposes, Upstate New York refers to that part of New York State which lies outside of Long Island and New York City. Are you not an Upstate New Yorker? We welcome you to join us at our training sessions, but can’t invite you to be part of our geographically-defined teams at ARML and other contests.
We’ll continue our problem review by focusing our attention on some recent AMC 10/12 contest problems. Join us on Sunday December 8 at 9am on Zoom: (https://bard.zoom.us/j/82682517748?pwd=y9JLpHLkj58ZhysTtIzUtHjWBty1ID.1)
Upcoming Practices
2024 AMC 10/12 Problem Review
Date: Sunday, December 8, 2024
Time: 9:00am - 10:00am (Just one hour.)
Zoom: Click Here (https://bard.zoom.us/j/82682517748?pwd=y9JLpHLkj58ZhysTtIzUtHjWBty1ID.1)
Description: Let's take an hour to share solutions to this year’s AMC 10/12 with each other. Japheth will host an hour’s worth of solutions. Let's emphasize clear and insightful solutions that are prepared in advance.
Coming up: Let’s continue our AMC 10/12 Problem Review on Sunday, December 15.
We hope you will join us!
Reminder: Please get ahold of a copy of Paul Zeitz’s Art and Craft of Problem Solving book, which we will use as a common text this year.
AMC 10/12 Problems
Get ready for the AMC 10/12 Problem Review by working on the problems. Here are links to the four AMC contests from earlier this month:
We don’t have time to review all the problems, but get ready for some nice solutions!
Update from the AMC:
Scores for the MAA AMC are released only to Competition Managers, not to the students directly.
Digital Administration: Official digital competition scores for each competition were released after 8 am ET the following day. Any scores viewed before that time were potentially incomplete or incorrect. Currently displayed scores are accurate and may be shared with students.
Print & Scan Administration: All answer sheets should be uploaded at this time. All scores are preliminary pending manual verification. We will announce your scores as finalized and official within the next few weeks. They should be shared with students at that time.
AIME qualifier thresholds will be announced by mid-December. Competition Managers of qualifiers will receive a separate email with more information at that time.
Calendar
Thursday, February 6, 2025: AIME I (by invitation)
Wednesday, February 12, 2025: AIME II (by invitation)
Wednesday/Thursday, March 19-20, 2025: USAMO/USAJMO (by invitation)
Saturday, April 5, 2025 (tentatively): NYSML at Syosset High School
Friday–Saturday, May 30–31, 2025: ARML at Penn State
Opportunities
Do you know of opportunities of interest to the Upstate New York Math Team members? Please send them our way!
Accolades
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