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#121 TemplateRex

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Posted 27 November 2017 - 11:14 AM

You could place all of them on the board. Technically, per the ISF, no piece threatens another piece unless it is adjacent to it. This includes scouts.

 

Per the ISF rules regarding multi-square chasing, you are correct. BTW, many of the other quiz problems posted in this thread, rely on the double chase defense, which is also not allowed per the ISF rules (but apparently not enforced in games on this site).

 

However, Napoleon 1er wrote in his original post (emphasis mine) that this quiz has to be interpreted as the generalization to the 8-queens puzzle to Stratego scouts. 

 

But before we start  I have 2 little preliminary quizz. You may know in chess the famous problem " How to place 8 Queens on a chess board without having any of the 8 queens threatening another one?".

On this forum the word threatening (or threaten) will mean "beeing in degree to attack, so in stratego it means a piece is threatening another one if it is placed on a directly neighbour cell (right, left, up or down), except for the scouts who can threaten from long distance horizontally or vertically as long as there is no obstacles in between.

 

 

Or if you want to be really mathematically precise: what is the independence number (the size of the maximum independent set) of the scout's graph on the Stratego board?

 

Similarly, there is another famous chess problem: how many queens are needed to reach every square in at most one move? This is known in mathematics as the domination number (the size of the minimum dominating set) of the queen's graph on the chess board. For the chess queen, the answer is 5; for the chess rook (which moves like the Stratego scout) the answer is 8.

 

In Stratego terms: what is the minimum number of scouts that have to be placed on the Stratego board so that every square can be scouted in at most one move? The answer is 8:

 

1hRmO3.png

 

It is left as an exercise for the reader to count how many different permutations of the 8 scouts dominate the entire board.


Edited by TemplateRex, 27 November 2017 - 11:18 AM.

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#122 OuweSok

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Posted 28 November 2017 - 09:31 AM

It is left as an exercise for the reader to count how many different permutations of the 8 scouts dominate the entire board.

 

Is 10x10x6x5x4x3x2 = 72000 the correct answer to this question?

 

I came to this reasoning: first piece must be put in one of 6 columns, second piece in one of 5 columns, third piece in one of 4, 3, 2, 1 and the last two pieces have complete freedom.


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#123 TemplateRex

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Posted 28 November 2017 - 11:57 AM

Is 10x10x6x5x4x3x2 = 72000 the correct answer to this question?

 

I came to this reasoning: first piece must be put in one of 6 columns, second piece in one of 5 columns, third piece in one of 4, 3, 2, 1 and the last two pieces have complete freedom.

 

The reasoning is partly correct. Here's my count: first you need to pick 6 out of 8 non-lake rows in which to place the first 6 scouts in the ABEFIJ columns. Or, equivalently, picking the 2 out of the 8 rows where there the remaining 2 scouts will be added later. This can be done in 28 ways = 8! / (6! * 2!). Then you indeed pick the 6 columns for the first 6 scouts: this has indeed 6! = 720 possibilities. Finally, you place the last 2 scouts in the remaining 2 open rows, and this can be done in any column, so indeed 10^2 = 100. Summarizing, I get 28 times your number = 2,016,000.

 

If I feel like it, maybe tonight I will run an exhaustive search over all choose(92, 8) = 93 billion (yes, 9 zeros) possibilities and get the definitive confirmation.


Edited by TemplateRex, 28 November 2017 - 11:58 AM.

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#124 OuweSok

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Posted 28 November 2017 - 10:18 PM

If this is the training and quiz thread I can put this, I suppose:

 

https://www.youtube....h?v=3cE4Me65rz4

Follow the game until 3:23, when I advance with my captain to the unknown piece. Why did I think that was a good idea?

 

https://www.youtube....h?v=FXSEpu2gUv4

Now follow the game until 3:29. What is your best guess for the front line piece your opponent moved. Why?

 

These are real life scenarios in normal games. If you want to get better, you need to be able to make deductions about your opponent's unknown pieces. The best way to learn this is to practice!


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#125 TheOptician

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Posted 28 November 2017 - 10:52 PM

If this is the training and quiz thread I can put this, I suppose:

 

https://www.youtube....h?v=3cE4Me65rz4

Follow the game until 3:23, when I advance with my captain to the unknown piece. Why did I think that was a good idea?

 

You figured it was likely to be worse than a captain as earlier when your major retreated it didn't take your unknown general

 

https://www.youtube....h?v=FXSEpu2gUv4

Now follow the game until 3:29. What is your best guess for the front line piece your opponent moved. Why?

 

I guessed scout. Not for any great reason. It had a lieut to its left and could have had a piece better than captain behind.



#126 OuweSok

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Posted 30 November 2017 - 09:00 PM

If this is the training and quiz thread I can put this, I suppose:

 

https://www.youtube....h?v=3cE4Me65rz4

Follow the game until 3:23, when I advance with my captain to the unknown piece. Why did I think that was a good idea?

 

 

 

You figured it was likely to be worse than a captain as earlier when your major retreated it didn't take your unknown general

 

 

Not many respond to these kind of questions. I think real game positions and extracting information is very important and a skill you must practice. I would gladly look at similar early game scenarios put by a platinum player.

 

Anyway, I reasoned that his captain retreated to the left when threatened by my major, so it is much less likely that the captain is protected at the entire right. If there is a colonel behind, he will not move the captain to the left and maybe expose his colonel to a scout. So therefore I expected the 2nd row piece to be < captain


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#127 Napoleon 1er

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Posted 30 November 2017 - 09:10 PM

for the first video at 3:23 you took that unknown lieut that has moved because you were already a cap and a lieut ahead, so you can sacrify a cap and either capture a smaller piece or gain information on a higher one while still maintaining material advantage.


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#128 TemplateRex

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Posted 17 February 2018 - 07:25 PM

RVAJgMJ.jpg

 

Red to move. Missing from the diagram: one extra blue sergeant

 

Quiz Nr. 1 by TemplateRex

  1. Place left-pointing arrows on the most distant squares where this extra sergeant can stand while still giving blue the win. (you can make diagrams from http://members.chell...ardeditor.html)
  2. what is the result if the extra blue sergeant is beyond this outer limit?

Please put your answer in spoiler tags.


Edited by TemplateRex, 17 February 2018 - 07:27 PM.

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#129 don mitsos

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Posted 17 February 2018 - 07:41 PM

I think if this extra sergeant is at A6 or A7 or A8, then blue wins. If not it is a tie



#130 Unladen Swallow

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Posted 17 February 2018 - 07:44 PM

Also a5 b7 b9 c7 and d7

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#131 don mitsos

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Posted 17 February 2018 - 07:56 PM

yes if the blue knows that the A10 piece is not a bomb



#132 TemplateRex

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Posted 17 February 2018 - 08:36 PM

Also a5 b7 b9 c7 and d7

 

You are on the right track, but it's still not the full answer :)


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#133 DarthRemark

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Posted 17 February 2018 - 08:50 PM

He can start as far away as I1 or J2 and win.  J1 is a draw.


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#134 TemplateRex

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Posted 17 February 2018 - 08:56 PM

He can start as far away as I1 or J2 and win.  J1 is a draw.

 

It's red to move in the diagram, I think you are off by one square. 


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#135 texaspete09

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Posted 17 February 2018 - 08:59 PM

If it is red's move, red has to move to B9. Blue knows the flag is in triangle, and knowing that B9 is not a scout, Blue moves to A8 to block scout. Then, red attempts to pass with miner, blue lets it go, and if you count pieces the furthest out the other sarge could be is I2 for the win.


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#136 DarthRemark

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Posted 17 February 2018 - 09:00 PM

You are right.  I was thinking blue moves first.  :)
 
He can start as far away as H1 or I2 and win. 

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#137 TemplateRex

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Posted 17 February 2018 - 09:25 PM



If it is red's move, red has to move to B9. Blue knows the flag is in triangle, and knowing that B9 is not a scout, Blue moves to A8 to block scout. Then, red attempts to pass with miner, blue lets it go, and if you count pieces the furthest out the other sarge could be is I2 for the win.

 

t13EDGA.jpg

 

Yes, your answer and reasoning is correct! If the extra blue sergeant is on the arrow squares or further to the left, blue can win by the variation that you point out. Otherwise, red can either pass a miner to blue's flag for a win, or he can free his scout for a draw.

 

The puzzle is inspired by a recent game of mine, where there were two more unmoved red pieces on the tenth row. The sergeant on B8 was a major, and I had a captain on F7. The game happened exactly as your variation, with the scout getting out. After taking the draw (I had only one more movable piece, also on the tenth row, so I couldn't trap his scout), I was racking my brain how I could have won, but the captain on F7 was two squares too far from blocking the miner.  

 

PS: the border of arrows determining the difference between draw/win is reminiscent of the Rule of the Square for chess pawn endgames: https://en.wikipedia...e_of_the_square Here it's similar: after red A9 blue A8, just extend a triangle from B2 and B9 and you find I2 as the outermost square. If the red miner is in the same tilted rectangle as the blocking piece, it can't reach the flag. You can use this rule to quickly determine how far your blocking pieces can stray away from the flag to block potential miners in endgames.


Edited by TemplateRex, 17 February 2018 - 10:06 PM.

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#138 TemplateRex

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Posted 03 March 2018 - 02:48 PM

MIqo98t.jpg

Quiz Nr. 2 by TemplateRex:


Blue's last move placed an hitherto unmoved captain next to a known red major. In the game, red captured on C8 and blue played his unknown scout to D9.
  • What devious plan could blue have with this sacrifice that freed up a back row piece?
  • What are red defenses after blue's move to D9?

Edited by TemplateRex, 03 March 2018 - 03:05 PM.

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#139 Don_Homer

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Posted 03 March 2018 - 03:40 PM

Nice situation mr Rex, maybe its too complicated though if many pieces are unknown to figure out what will happen (too many possibilities). With all known pieces blue tries to get the flag with scout behind marshall. But red can probably defend with his scout and eventually win the game.

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#140 Unladen Swallow

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Posted 03 March 2018 - 03:52 PM

Yes red can defend easily. You can accept that gambit. It's unsound. 


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