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#261 - Sniper -

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Posted 03 July 2018 - 08:17 PM

Seems adaptation of https://en.wikipedia...t_queens_puzzle

 

Maybe the same solution applies?



#262 TemplateRex

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Posted 03 July 2018 - 10:17 PM

Seems adaptation of https://en.wikipedia...t_queens_puzzle

 

Maybe the same solution applies?

 

Not quite: http://forum.strateg...forum/?p=441845

 

There are many related scout puzzles posted here. Napoleon 1er, Max Roelofs, The Prof, and I posted the following puzzles:

  1. maximum number of scouts that all threaten exactly 0 other scouts (answer: 14, this is the problem equal to N-queens)
  2. maximum number of scouts that all threaten exactly 1 other scout (answer: 18)
  3. maximum number of scouts that all threaten exactly 0 other scouts in the presence of 6 bombs in each 4x10 starting box (answer: unknown, not been posted here)
  4. minimum number of scouts so that every squares is threatened at least 1 times (answer: 8, in chess it's 5 for queens, 8 for rooks)

I have written a small Python program that calls a mathematical solver (Z3) to check all possibilities. I can post the source code if anyone is interested.

 

Problems 1 and 4 were solved within 1 second. The problem 2 took about 80 minutes before the computer proved that 18 was the max. I haven't tried to solve problem 3 yet. The number of configuration is enormous (10^16, 10^19, 10^11 for problems 1, 2, 4 and 10^32 for problem 3). I don't think problem 3 is solvable by brute force, not even with clever mathematical solvers like Z3. 


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#263 TemplateRex

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Posted 11 July 2018 - 11:05 AM

I released a Python repository on GitHub for solving N-queens type puzzles on a Stratego board using the Z3 SMT-solver. The hard problem of mutually covering scouts has been reduced to 20 minutes now (4x speedup).


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#264 TemplateRex

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Posted 16 July 2018 - 05:52 PM

Hi The prof. My answer to your extension of preliminary quizz N°1 is: I have a solution for 22 scouts but I'm not sure it is the maximum ... :P

Napoleon 1er

It turns out that the maximum that can be obtained is to place 24 scouts, with 6 bombs in each setup side.

. . . 2 B 2 . . . . 
. . 2 B 2 B 2 . . . 
. . . 2 B 2 B 2 . . 
. . . . 2 B 2 . . . 
2 . # # . . # # 2 . 
. . # # . 2 # # . 2 
. . . 2 . B 2 . . . 
. . 2 B . 2 B 2 . . 
. 2 B 2 B . 2 . . . 
. . 2 B 2 . . . . .
The above solution was obtained by math professors Zantema and Wesselink from the university of Eindhoven, the Netherlands. The latter person is a former Dutch champion of draughts whose help I enlisted on how to handle these bomb/scout placement puzzles. My own programming skills were enough to solve the puzzles by Napoleon 1er and maxroelofs, but the one from The Prof required some very clever programming tricks from real professors :)

Edited by TemplateRex, 16 July 2018 - 05:55 PM.

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#265 TemplateRex

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Posted 03 August 2018 - 09:07 PM

I released a Python repository on GitHub for solving N-queens type puzzles on a Stratego board using the Z3 SMT-solver. The hard problem of mutually covering scouts has been reduced to 20 minutes now (4x speedup).

 

My Python repository on GitHub of the various scout/bomb placement puzzles is now in maintenance mode. All 6 problems can be solved within reasonable time (mostly 1 second, and 15 minutes for the hardest puzzle, which is known to be solvable within 10 seconds using a more sophisticated approach than I cared to implement). The README shows all solutions and contains links to the original posts on this forum. Thanks everyone here (Napoleon 1er, maxroelofs and The Prof) for posting these hard problems. I learned some nice new programming skills!  :)


Edited by TemplateRex, 03 August 2018 - 09:08 PM.

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#266 TemplateRex

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Posted 18 August 2018 - 03:34 PM

2GcU1yQ.jpg

 

Blue to move, all pieces known.

 

Quiz Nr. 5 by TemplateRex

 

1) How can blue win this position?

2) How can red draw this position with the flag on D1 instead of E1 (still with blue to move)?

3) How can red draw this position with the flag on F1 instead of E1 (still with blue to move)?


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#267 Napoleon 1er

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Posted 18 August 2018 - 04:23 PM

Not sure to understand. For me blue wins always

E6-E5 E7-F7
F6-E6 F7-E7
... then as soon as the red lieut will have exceeded the number of moves allowed by 2square rule he will be forced to move out from the zone F7 and E7. This will allow blue to get out with a sergeant and then go to the flag.
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#268 TemplateRex

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Posted 18 August 2018 - 04:30 PM

Not sure to understand. For me blue wins always

E6-E5 E7-F7
F6-E6 F7-E7
... then as soon as the red lieut will have exceeded the number of moves allowed by 2square rule he will be forced to move out from the zone F7 and E7. This will allow blue to get out with a sergeant and then go to the flag.

 

Red can keep the lieut on E7, move around with his spy... how does blue win then?


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#269 KissMyCookie

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Posted 18 August 2018 - 06:12 PM

Blue to win:

F6 to F7–red lieutenant must take:

E8 to E7–red lieut. must take again;

F8 to F7–Red must take but is then stuck on two square rule;

E6 sergeant can move out and get to Red's flag before red can protect it.

 

I think that this is correct.


Edited by KissMyCookie, 18 August 2018 - 06:13 PM.

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#270 KissMyCookie

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Posted 18 August 2018 - 06:20 PM

Red to draw with Red Flag on D1:

 

Blue must move either F6 or F8 to start–Red lieut. takes piece;

Either E6 or E8 is moved by Blue–Red takes;

Blue moves remaining F row sergeant–Red takes remaining E row sergeant;

 

Race to flag, blue cannot get there before Red is on E to protect it.

 

The same principal of this solution for the flag on F1 applies in the same way, only it plays out similar to Blue to win–two square kicks in, but red can get to protect the flag at F1 in this scenario.

 

Please let me know if I have misunderstood your puzzle challenge, Template Rex...this is a very good and fun mind-bender. :)


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#271 TemplateRex

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Posted 18 August 2018 - 07:44 PM

Red to draw with Red Flag on D1:

 

Blue must move either F6 or F8 to start–Red lieut. takes piece;

Either E6 or E8 is moved by Blue–Red takes;

Blue moves remaining F row sergeant–Red takes remaining E row sergeant;

 

Race to flag, blue cannot get there before Red is on E to protect it.

 

Yes, here red has to race from E6 or E8 to E2 (12 moves around the left lake) to block the last blue sarge who starts the race from F7 to F1 (12 moves around the right lake). So red is just in time to block access to the D1 flag.

 

The same principal of this solution for the flag on F1 applies in the same way, only it plays out similar to Blue to win–two square kicks in, but red can get to protect the flag at F1 in this scenario.

 

Yes, here red starts the race from F7 to E2 (12 moves around the right lake) to block the last blue sarge who races from E7 to D1 (11 moves around the left lake). Again, red is just in time to block acces to the F1 flag.

 

Please let me know if I have misunderstood your puzzle challenge, Template Rex...this is a very good and fun mind-bender. :)

 

Thanks to Don Homer for challenging me to find a situation where the current ISF-rule of 3 repetitions over 2 squares gives a different result than the old ISF-rule where up to 5 repetitions was allowed :)


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#272 Don_Homer

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Posted 19 August 2018 - 02:16 PM

2GcU1yQ.jpg

 

Blue to move, all pieces known.

 

Quiz Nr. 5 by TemplateRex

 

1) How can blue win this position?

2) How can red draw this position with the flag on D1 instead of E1 (still with blue to move)?

3) How can red draw this position with the flag on F1 instead of E1 (still with blue to move)?

1; offer the 3 sercheants and go for the flag with the 4th.

3. The same, cause red will be on time to stop the sercheant, the sercheant will back away and its a draw.
2. Use The Don-Strategy. Pick up 2 offered sercheants, dont get the 3th but choose the other one and run the other way round to be just in time to stop blue.

 

I think its clear this way I prefer to not use the notations to prevent (more) errors :)


Edited by Don_Homer, 19 August 2018 - 02:17 PM.

Molto Bene, Thats a nica Donut !


#273 KissMyCookie

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Posted 19 August 2018 - 04:01 PM

1; offer the 3 sercheants and go for the flag with the 4th.

3. The same, cause red will be on time to stop the sercheant, the sercheant will back away and its a draw.
2. Use The Don-Strategy. Pick up 2 offered sercheants, dont get the 3th but choose the other one and run the other way round to be just in time to stop blue.

 

I think its clear this way I prefer to not use the notations to prevent (more) errors :)

 

You're a little late to the party . . .  :D  But I appreciate your quoting my solution . . .  :lol:


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#274 Napoleon 1er

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Posted 19 August 2018 - 07:10 PM

the above case is almost unreal. Better to have cases that are part of real battles


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#275 TemplateRex

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Posted 19 August 2018 - 07:25 PM

the above case is almost unreal. Better to have cases that are part of real battles

 

In chess, there's a long tradition of puzzles that are far removed from practical play, instead emphasizing unique themes. I agree that for training purposes, regular game situations are more useful. However, since this is the quiz and training forum, with several other curiosa (in particular the very nice scout and bomb placement puzzles that you initiated!) I thought it would be appropriate to post this two-square rule puzzle :)


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#276 KissMyCookie

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Posted 19 August 2018 - 09:25 PM

the above case is almost unreal. Better to have cases that are part of real battles

 

I disagree with you, Daniel. Perhaps your expectations got in the way of your ability to view the puzzle objectively.

 

Max Roelofs would often create immensely challenging puzzles for me to work out when I was taking lessons from him. They would not necessarily reflect an actual situation on the Stratego board (but some did to amazing effect), but Max was intelligent and visionary enough to apply principals of the game to the puzzle administered.

 

In this case, Template Rex offers us a perfect illustration of how the two-square rule would come into effect and determine the outcome of the match–this is a very, VERY clever puzzle. It goes right to the heart of one of the most important aspects of playing (offensively and defensively) Stratego–the Two-Square Rule.

 

So you see...even a master of this game, such as yourself, can still learn a thing or two about Stratego from those of us still climbing the ranks. :lol:  :lol:  :lol:

 

KMC :ph34r:



#277 Napoleon 1er

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Posted 08 September 2018 - 08:17 AM

yesterday i was in the following position with blue:

 

qEyL8BG.jpg

 

the game ended as a draw but i wonder if somebody has a solution to make it end as a win?

blue has the move


Edited by Napoleon 1er, 08 September 2018 - 08:19 AM.

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#278 TemplateRex

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Posted 08 September 2018 - 10:37 AM

yesterday i was in the following position with blue:

 

qEyL8BG.jpg

 

the game ended as a draw but i wonder if somebody has a solution to make it end as a win?

blue has the move

 

First, the two red pieces must be a flag and a bomb, otherwise the captain can just hit both of them unopposed. Second, the captain can always make a gamble on one of the two and get 3.5 points on average. Third, blue can offer a draw for 3 points :)

 

For a guaranteed win, the miner needs to hit either on G10 or H10, and the captain can then hit on the other. But the red scout seems to give red a big advantage since any blockade can be maintained forever by making scout moves. E.g. after B5-B6-B7-C7-D7 (4 moves), blue moves F4-F5-F6-F7-E7 (4 moves) and I can't see how blue can make progress. 

 

Seems a draw to me.


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#279 Napoleon 1er

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Posted 08 September 2018 - 12:07 PM

yes, i confirm the 2 reds on G10 and H10 are flag and bomb. if all movable pieces would be in same positions but symmetrically reversed on right side then i guess it would be a win ... but how could i reverse from this position to get the same on the right?


Edited by Napoleon 1er, 08 September 2018 - 12:12 PM.

If you don't know where you go ... you have a lot of chance to arrive elsewhere ...

#280 TemplateRex

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Posted 08 September 2018 - 12:28 PM



yes, i confirm the 2 reds on G10 and H10 are flag and bomb. if all movable pieces would be in same positions but symmetrically reversed on right side then i guess it would be a win ... but how could i reverse from this position to get the same on the right?

 

ogYUDCX.jpg

 

Indeed, after

1. I5-I6 E4-E5

2. I6-I7 E5-E6

3. G8-H8 H9-I10

4. H8-I8 I10-J10

5. I7-H7 E6-E7

5. H7-H8 etc. and blue wins

 

Maybe if the blue sergeant is 2 squares closer to the lakes, it will again be impossible for blue to get to the flag.


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