(25) N-Queens
03-02-2022, 01:20 AM
Post: #1
 Thomas Klemm Senior Member Posts: 2,068 Joined: Dec 2013
(25) N-Queens
References
The program is based on the flowcharts that are linked in Dave Britten's solution.
But I had to make some changes:
• the number format is $$0.a_1 a_2 \cdots a_8$$
• the indexes $$m_0$$ and $$m_1$$ are decremented so we can use comparison with $$0$$
• the number $$10$$ is kept as a constant in register $$m_6$$
• storage arithmetic helped to save some steps

Registers

0: # of old queens
1: New queen
2: Old queens
3: Chopping block
4: i counter
5: n size of board
6: 10 as constant

Initialization and Run

CLEAR REG
FIX 8
8
STO 0
STO 5
10
STO 6
GTO 13
R/S

Solution

After about 40 minutes this result is shown:

0.57263148

This corresponds to the following setup:

5 7 2 6 3 1 4 8
8: | | | | | | | |#|
7: | |#| | | | | | |
6: | | | |#| | | | |
5: |#| | | | | | | |
4: | | | | | | |#| |
3: | | | | |#| | | |
2: | | |#| | | | | |
1: | | | | | |#| | |

The next solutions will be shown after starting the program again with R/S.
However for now it will not detect the end.
There simply was no memory left to do so.

Program

The program can be used in this HP-25C emulator.
Code:
01: 24 01    : RCL 1 02: 23 51 02 : STO + 2 03: 24 06    : RCL 6 04: 23 71 02 : STO / 2 05: 01       : 1 06: 23 41 00 : STO - 0 07: 24 00    : RCL 0 08: 15 61    : g x<>0 09: 13 13    : GTO 13 10: 24 02    : RCL 2 11: 74       : R/S 12: 13 36    : GTO 36 13: 24 05    : RCL 5 14: 23 01    : STO 1 15: 24 02    : RCL 2 16: 23 03    : STO 3 17: 34       : CLx 18: 23 04    : STO 4 19: 01       : 1 20: 23 51 04 : STO + 4 21: 24 06    : RCL 6 22: 23 61 03 : STO * 3 23: 24 03    : RCL 3 24: 15 71    : g x=0 25: 13 01    : GTO 01 26: 14 01    : f INT 27: 23 41 03 : STO - 3 28: 24 01    : RCL 1 29: 14 71    : f x=y 30: 13 36    : GTO 36 31: 41       : - 32: 15 03    : g ABS 33: 24 04    : RCL 4 34: 14 61    : f x<>y 35: 13 19    : GTO 19 36: 01       : 1 37: 23 41 01 : STO - 1 38: 24 01    : RCL 1 39: 15 61    : g x<>0 40: 13 15    : GTO 15 41: 01       : 1 42: 23 51 00 : STO + 0 43: 24 06    : RCL 6 44: 23 61 02 : STO * 2 45: 24 02    : RCL 2 46: 14 01    : f INT 47: 23 41 02 : STO - 2 48: 23 01    : STO 1 49: 13 36    : GTO 36
03-02-2022, 01:31 AM
Post: #2
 Dave Britten Senior Member Posts: 2,307 Joined: Dec 2013
RE: (25) N-Queens
Wow, impressive! I took a very brief stab at doing this, but I was about 20 steps over the limit, with no obvious way to trim any more fat.
08-03-2023, 12:44 PM
Post: #3
 Stefan Falk Junior Member Posts: 25 Joined: May 2021
RE: (25) N-Queens
This is really freaking cool. I've done N Queens on each and every calculator and computer (from the HP 9820 in school on) I had under my fingers (not yet on the HP Prime), and am just working on it on my "new" 48GX. I read that it has been done on the HP-65, which is fantastic enough. But on the HP-25 - amazing, unbelievable! Chapeau!

Best Regards,
Stefan
08-05-2023, 11:39 AM
Post: #4
 Thomas Klemm Senior Member Posts: 2,068 Joined: Dec 2013
RE: (25) N-Queens
(08-03-2023 12:44 PM)Stefan Falk Wrote:  I've done N Queens on each and every calculator (…) I had under my fingers …

You might also like a this solution: N-queens benchmark and the HP-17BII
Both are listed in the Calculator Speed Benchmark using the N-Queens Problem.

Here's my solution for the HP-25 in the thread: Weakest calculator/pocket computer that can do Tower of Hanoi?
It shows how much can be done despite the limitations.
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