Since 2014, Exact Science's teacher have hosted unique camps in Mathematics and Programming, offering a rich mix of learning materials, problem sets, and a diverse group of teachers and participants. This year, Exact Science launched its first Olympiad Mathematics Camp.
Over six days (28 - 30 December 2023 and 2 - 4 January 2024), our students attended daily seminars to understand approaches to Olympiad Problems in various mathematical fields and how AI, specifically ChatGPT, solves them.
Our excitement peaked with the introduction of the AIMO Prize:
XTX Markets is launching a new $10mn challenge fund, the Artificial Intelligence Mathematical Olympiad Prize (AIMO Prize). The fund intends to spur the development of AI models that can reason mathematically, leading to the creation of a publicly-shared AI model capable of winning a gold medal in the International Mathematical Olympiad (IMO).
Today, I want to demonstrate how ChatGPT attempts to solve Olympiad problems for ages 10-12 in these topics:
We started with a simple cryptarithm problem, which was also one of our Problem of the Day.
“In this cryptarithm: BAO×BA×B=2002. What are the values of B, A, and O?“
ChatGPT's first step already led to an incorrect conclusion!
The correct first step would be to understand the prime factorisation of the number:
2002 = 2 × 1001
1001 can be easily mistaken for a prime number, but it is actually a product of 7 × 11 × 13.
So, 2002 = 2 × 7 × 11 × 13
From there, it is a matter of logic and a few attempts to find the solution.
Try to find it yourself!
Parity is an ideal topic for expanding understanding of numbers being odd or even.
After covering the theoretical part, we gave ChatGPT this problem:
“Numbers from 1 to 10 are written in a row. Is it possible to place “+” and “–” signs between them so that the value of the resulting expression is zero?”
We assumed that ChatGPT, with its powerful computational abilities, could easily iterate through all possible combinations of “+” and “-”. Surprisingly, this was its response:
After calculating its answer, we got this:
1+2−3+4−5+6−7+8−9+10 = 7.
In fact, the answer to this problem is “No, it is not possible”. The explanation is simple when approached from a Parity perspective.
If you add/subtract five odd and five even numbers, you will never get an even number, which in this case is 0. And yes, zero is an even number. We checked.
“A farmer wants to cross a river and take a wolf, a goat, and a cabbage with him. There is a boat that can fit himself plus either the wolf, the goat, or the cabbage. If the wolf and the goat are left alone on one shore, the wolf will eat the goat. If the goat and the cabbage are left alone, the goat will eat the cabbage. How can the farmer bring the wolf, the goat, and the cabbage across the river?”
I personally thought that, given the popularity of this problem and ChatGPT being a Large Language Model, it could just recreate the solution from various sources. But this was its response:
It seemed fine after the first two logical statements, but then it started to lose track after “The farmer leaves the goat on the other side and takes the wolf back.”
ChatGPT did manage to correctly produce the first couple of statements, but it was a shame it didn’t finish it correctly.
I have never been a fan of this type of problem in Maths or Programming Olympiads, but we were very curious about ChatGPT's response.
The problem we chose was from the Junior Mathematics Challenge 2018, Question 3. It seemed to be one of the simpler problems at our camp, so we gave it to the AI for a solution attempt.
Once again, the AI was on the right track but failed to reach the correct conclusion. It was fortunate that the question was multiple-choice; otherwise, it might not have realized its answers were incorrect.
ChatGPT seems to be struggling with his own logic, while the answer is obviously 60 + 45 = 105.
We had not previously tested these problems, aiming to select ones that AI, computers, or ChatGPT could more easily understand and, hopefully, solve.
As for AI solving the International Maths Olympiad, it seems unlikely that this will happen in the near future.
Ask about our courses and offerings, and we will help you choose what works best for you.
