This is the count donut problem. Given a grid of 1s and 0s where 1 represents land and 0 represents water find the amount of donuts. A donut is an island with at least one hole in it. Two grid cells that are diagonal or adjacent form a barrier that water cannot cross. Count the amount of donuts in the grid.

This is a unique problem I came up with. It’s a variation on counting islands. There are actually two correct answers that are straightforward. Other answers may exist but are generally not straightforward and often wrong. One answer is mathematical the other is a leetcode style solution.

Try to solve this yourself before using ai to get a feel for how hard it is. The solution should be extremely straightforward. It’s also fun to think about. When you try to think of a solution you will invariably come up with a bunch of possible solutions that are wrong which is a strong indicator of how large the range of possible answers are. Few answers are correct but many look correct.

I give this test to candidates and I never expect the candidate to solve it because it’s one of the few algorithms that requires actual reasoning and actual creativity as I came up with it so no variation of it really exists anywhere else. You can’t pattern match for it. Out of like 50 candidates you probably get one person able to solve it in less than an hour.

It’s unlikely most people on hn will be able to solve it. If you do solve it don’t post the answer as it will become training data for the next iteration of the LLM.

I gave the prompt to o3. It solved. It generated code as well which I was too lazy to verify but it solved it correctly in the description of the algorithm involved.

There is also a 3D version of this problem where the grid is 3D. It changes the entire problem if a donut is in 3D space. It is harder and I have only found one possible solution for it. I have not tried it on an LLM.