PRIMES STEP
PRIMES STEP students with Dr. Tanya Khovanova and PRIMES Chief Research Advisor Prof. Pavel Etingof, Sixth Annual PRIMES conference, May 2016, MIT.
PRIMES STEP students' research papers
- "Who Is Guilty?" (2016)
- Alternator Coins (2016), published in Math Horizons 25:1 (2017): 22–25
- On Variations of Nim and Chomp (2017), published in The Minnesota Journal of Undergraduate Mathematics 4:1 (September 2018)
- PRIMES STEP Plays Games (2017), published in Math Horizons 26:2 (2018): 10–13
- On Base 3/2 and its Sequences (2018)
- Variants of Base 3 over 2 (2018), published in Journal of Integer Sequences 23 (2020)
- Chip-Firing and Fractional Bases (2018)
- It's Common Knowledge (2019), published in Recreational Mathematics Magazine 6:12 (2019): 9–32
- The No-Flippancy Game (2020)
- The Classification of Magic SET Squares (2020), published Recreational Mathematics Magazine 7:13 (2020): 71–94
- From Unequal Chance to a Coin Game Dance: Variants of Penney's Game (2020)
- Confirming the Labels of Coins in One Weighing (2020)
Try these problems Problem 1. Mrs. Fullhouse has 2 sons, 3 daughters, 2 cats and 1 dog. How many children does she have?
Problem 2. Detective Radstein is investigating a robbery. He apprehends three suspects: Anne, Bill, and Caroline. The detective knows that no one else could have participated in the robbery. During the interrogation the suspects make the following statements: Anne: I didn't do it. Bill did it alone.
Bill: I didn't do it. Caroline did it. Caroline: I didn't do it. Bill did it.
Problem 3. One day you meet your friend Alice enjoying a nice walk with her husband Bob and their son Carl. They are excited to see you and they invite you to their party. Alice: Please, come to our party on Sunday at our place at 632 Elm St. in Watertown.
Bob: My wife likes exaggerating and multiplies every number she mentions by 2. Carl: My dad compensates for my mom's exaggerations and divides every number he mentions by 4. Alice: Our son is not like us at all. He doesn't multiply or divide. He just adds 8 to every number he mentions.
Problem 4. There are n ants placed randomly on a stick that is 1 meter long. The ants immediately start running along the stick, choosing a random direction, either left or right, with the same constant speed equal to 1 meter per second. When two ants bump into each other they immediately reverse direction, and continue running with the same speed. When an ant reaches the end of the stick it falls off. What is the expected time for the stick to become completely free of ants? |
What is PRIMES STEP? PRIMES STEP (Solve–Theorize–Explore–Prove) is your step into the world of mathematical discovery. It is a program for curious middle-schoolers who like solving challenging problems and are ready to explore advanced math topics. The goal of our program is to use mathematics to expand the students' minds and encourage their creative thinking. We will not repeat the middle-school math curriculum. We will solve a lot of problems that are tricky, logical, fun, and might potentially be asked at a Wall Street interview. See some examples in the left column. In addition to solving problems like these, we will cover some ideas and methods for solving olympiad-style problems. We will also try to simulate the research process by inventing new problems and being the first to solve them. We will even learn an occasional magic trick. The main goal is to have fun! The instructor is Dr. Tanya Khovanova, an active researcher in the field of recreational mathematics. There are two groups of students, which meet on Mondays or Thursdays, 6-8 pm, on MIT campus (during the COVID-19 pandemic all meetings are on Zoom). Research papers authored by PRIMES STEP students were featured on the American Mathematical Society blog. Tanya Khovanova is Lecturer in the Mathematics Department at MIT. She received her Ph.D. in mathematics from Moscow State University in 1988, under Israel Gelfand. Her research was in representation theory, integrable systems, quantum groups, and superstring theory. Currently she is interested in combinatorics and recreational mathematics. Dr. Khovanova is Head Mentor of math research at MIT PRIMES and MIT's Research Science Institute (RSI). She has created the popular Number Gossip site. Admissions Students entering 7th-9th grade in September and home schooled students of the same age are eligible. One letter of recommendation is required. Application for the 2020/21 academic year is now closed. Application for the 2021/22 academic year will open in April 2021. For preparation, we recommend studying books in the Art of Problem Solving series, as well as the 2015 STEP entrance test and its solutions, and the 2016 and 2017 entrance tests (later tests and solutions will not be posted). STEP sessions will be held online via Zoom during the fall term. Decision on the format of the spring term sessions will be made later in the fall. The sessions will be held on either Mondays or Thursdays, 6-8 pm. Tuition for the 2020/21 academic year is $2,100 per year, including $100 registration fee and two installments of $1,000 (due in September and in January). Need-based scholarships are available for families receiving public assistance. If you have any questions about your application, please contact PRIMES Admissions Assistant André Dixon at aldixon@mit.edu. |
With general questions about the program, please contact PRIMES Program Director Dr. Slava Gerovitch at primes.step@gmail.com