I like problems and riddles where you need very little background knowledge (and that's why I don't like the question "is the Riemann hypothesis true?" as a riddle) and very little knowledge to solve them (and that's why I don't like the riddle "what city is the capital of Guatemala?"), but where the solution requires using your head. Especially if the riddle isn't so much about coming up with an idea (and that's why I don't like calculating integrals), but more about not getting lost in the structure you build in your head. A few days ago, I came up with a riddle that fits these conditions nicely. The riddle goes:
We have two hypotheses. Hypothesis A says that every even natural number is the sum of two prime numbers. Hypothesis B says that every odd number is the sum of three prime numbers. Does either of these hypotheses follow from the other?
This riddle only requires elementary school knowledge, but intellectually it is more at a high school level.
When I asked an AI for more riddles of this type, it gave me a few, and these were the ones I liked the most:
Hypothesis A: In any group of 10 people, there are always 3 people who know each other.
Hypothesis B: In any group of 11 people, there are always 3 people who know each other.
Hypothesis A: Any square can be cut into exactly 4 smaller squares.
Hypothesis B: Any square can be cut into exactly 10 smaller squares.
Hypothesis A: Any natural number can be multiplied by an integer so that the result consists only of ones (e.g., 11, 111, 1111, etc.).
Hypothesis B: Any natural number can be multiplied by an integer so that the result consists only of threes (e.g., 33, 333, 3333, etc.).
Hypothesis A: Every number consisting only of ones (11, 111, 1111, 11111, etc.) is divisible by 3 with no remainder.
Hypothesis B: Every number consisting only of nines (99, 999, 9999, 99999, etc.) is divisible by 27 with no remainder.