Recent content by hariz91

My apologies, I made a calculation mistake - 1, [2], 1 → gives 0 - 1, 2, [3], 2, 1 → gives 3 - 1, 2, 3, [4], 3, 2, 1 → gives 8 - 1, 2, 3, 4, [5], 4, 3, 2, 1 → gives 15 ... - 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1 → gives 63 I'm sorry...

Thanks for the question. I got those results from a simple process I’ve been playing with: 1. I imagine 0 as a source that releases the value 1, one after another. 2. The first 1 appears — it’s just there. 3. When the second 1 appears, the two 1s interact and produce a new value: 2. They form a...

I’ve been exploring number patterns as a personal interest — particularly symmetric sequences like 1, 2, 1 or 1, 2, 3, 2, 1. I noticed that the middle value in these sequences sometimes seems to produce a new number when combined in a certain way. For example: - 1, [2], 1 → gives 0 - 1, 2, [3]...

Thanks @pbuk for the detailed breakdown! That clearly separates the confusion between finding a single solution vs enumerating all solutions. I see where my analogy fell short regarding the haystack example—scaling N is indeed more about expanding the search space itself rather than adding...

Is there any other problem as simple as placing queens on an N×N board?. Does admitting to difficulties in finding a solution count as failure? Is the idea of a shortcut dismissed by the majority, or is it still considered possible? If there is no shortcut, why does it involve calculations at...

‎Thank you for your response,@pbuk. I appreciate the clarification about fundamental solutions and the known symmetry properties of N-Queens. ‎ ‎I understand that rotations and reflections of solutions are well-documented, and I agree that this is not a new observation. ‎ ‎My interest lies more...

For N=4, each solution has exactly 4 non-attacking queens on the board (as you correctly said, the number of queens equals the board size N). What I meant by '8 queens' is the total number of queens across all solutions. Since N=4 has 2 solutions, I was imagining placing each solution on a...

N-Queens: Total Queen Count Patterns I've been studying N-Queens solutions and noticed something about the total number of queens across all solutions. For example, N=4 has 2 solutions. Total queens = 2 × 4 = 8. This is like preparing 2 separate 4×4 boards and placing one solution pattern on...