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I remember being given another puzzle in my childhood, where the task was to put 8 queens on the board and none of them should "see" each other. Wonder how many solutions exist for that one..
ETA: Apparently it's a classic puzzle, and there are 92 solutions - https://en.wikipedia.org/wiki/Eight_queens_puzzle
I didn’t find it that difficult. A good (?) guess is that the queens would be in (rotational) symmetry, and hence form a square. To maximize coverage, the angle of course is neither 90° nor 45°, and the queens will have a minimum distance of 3 from each other. Going from smallest distance possible between queens to largest, one tries (3, 1), (3, 2), (4, 1), done. One might not notice that (4, 1) works (which happened to me), because it only works when the square is at the edge of the playing field. But the next one, (4, 2), works unconditionally. Or going from largest to smallest, one tries (6, 1), (5, 2), (5, 1), (4, 3), (4, 2), done.
Neat. Surprisingly, there are 388 solutions, and a lot of them look rather unintuitive. ........ ...Q.... ........ ........ .....Q.. ........ ........ Q..B..Q. Q....... ........ ........ ........ ..QQB..Q ........ ........ ........ My original intuition was to place the queens on unique rows and columns to cover as much as possible but it turns out there are solutions with three of them on the same row. Python script…
That got me down to 6 free spaces.
- ChatGPT was able to solve it in 6 seconds.
- Opus exhausted my entire days token limit on the problem & didn’t solve it.
Neat. Surprisingly, there are 388 solutions, and a lot of them look rather unintuitive. ........ ...Q.... ........ ........ .....Q.. ........ ........ Q..B..Q. Q....... ........ ........ ........ ..QQB..Q ........ ........ ........ My original intuition was to place the queens on unique rows and columns to cover as much as possible but it turns out there are solutions with three of them on the same row. Python script…
After identifying solutions up to rotation and reflection there are only 49 solutions. No solutions have rotational symmetry, and there is exactly one solution with reflection symmetry (already mentioned by an earlier commenter).
Out of the 49 solution classes, there are 18 distinct queen layouts. The layouts have between 1 and 5 ways to place the bishop to complete the solution. Interestingly, there is exactly one queen layout (up to rotation / reflection) for which there are exactly 2 ways to place the bishop to complete the puzzle.
Neat. Surprisingly, there are 388 solutions, and a lot of them look rather unintuitive. ........ ...Q.... ........ ........ .....Q.. ........ ........ Q..B..Q. Q....... ........ ........ ........ ..QQB..Q ........ ........ ........ My original intuition was to place the queens on unique rows and columns to cover as much as possible but it turns out there are solutions with three of them on the same row. Python script…
is there a solution where all the pieces are covered as well?
The trick for me was to place a queen (most anywhere, but start with a corner it’s easier), then check and look for the spot with the most reds around it (eg 9, or 8, or 7), place the next queen there, repeat. Then place the bishop as needed. The key was realizing the proximal spaces next to the placed queen are the most important to cover. Forget about trying to have a long reach, it comes naturally.
This is an interesting test for LLMs. - ChatGPT was able to solve it in 6 seconds. - Opus exhausted my entire days token limit on the problem & didn’t solve it.
This is an interesting test for LLMs. - ChatGPT was able to solve it in 6 seconds. - Opus exhausted my entire days token limit on the problem & didn’t solve it.