> solve an applied problem you've never heard of or to sketch a proof to a given...

tuukkah · on Jan 20, 2024

I hear these problem types are not as common as they used to be, but here's some recent examples in this direction.

Fall 2023: "Prove that 2^12345678910 - 1 is divisible by 1023."

Spring 2022: "Using induction, show that the sum of the numbers on the line n of Pascal's triangle equals 2^n."

Here's the full exam from fall 2023: https://yle.fi/plus/abitreenit/2023/syksy/matematiikka_pitka...

apwell23 · on Jan 20, 2024

I cannot seem to access that link outside finland.

That is indeed a tough proof to solve sight unseen. Any reason you say that students are seeing that question for the first time in the test. Seems like a famous questions, even chatgpt got the proof correctly .

tuukkah · on Jan 20, 2024

I think the pressing question here is what the Anki cards contained w.r.t. these problems :-)

The high school curriculum and the text books are not focused on proofs or famous questions. Further, the goal of the exam is to find out your position in the normal distribution of your peers' math skills. You are not supposed to be able to beat everyone else by rote learning (so if you can do it, it's quite a hack!).

I don't think ChatGPT is a good comparison, because it has obviously memorized much more than a human could, and a test to poke its strengths and weaknesses would look different.