Answer to Preliminary QUizz N°1 by Napoleon 1er is: The maximum number of scouts that can be placed on a Stratego board without having anyone thresthening another is 14, see setup attached
Stratego quizz and training forum - ANSWERS
Posted 09 February 2014 - 10:53 AM
Posted 09 February 2014 - 11:01 AM
Answer to preliminary quizz N°2 by Napoleon 1er is: see setup attached. There are 4 symmetrical possibilities.
Posted 09 February 2014 - 11:03 AM
... By the way did you find the solutions for the 8 queens on a chess board? ... This forum is for stratego quizz only ... so if you want the answer you may certainly google it.
Posted 27 February 2014 - 10:23 PM
Answer to Quizz number 1 by Napoleon 1er - The danger of the chat
First of all let me explain the title "The danger of the chat". In this particular case, with the vision of the game I had, the first thought is that the flag is in I1 behind 3 bombs, so with my 3 miners against 2 captains and 1 sergeant I have no chance to win and almost any move I make would be unsuccessful. Then when my opponents unexpectedly asked my for a tie the whole game took another dimension, it's like he gave me all his secret information through the chat and without noticing it, now I knew that because he asked me for a tie it means that he was convinced that he couldn't win, and this case can only be if the last sergeant is plugged behind bombs and if it is so it means that the flag is open in F1, G1 or H1, in other words I may have some chance to win. So if my opponent believes that he cannot win let him think that even the draw is not possible for him and reply in this way in the chat in such a way that flag in H1 is also excluded, possibly he will surrender. And that what's happened.... but it was a bluff from me:
1) If red has to play the outcome of this game is a draw. Let's explain: if he first plays his captain in A3 he can bring it to D3 while you bring your miner from E6 to E4. Afterwards he can continuously double chase your miner in E4 or in J5 without leaving you any other opportunity than to move backwards. ANd if you do so he will have all time to bring his captains closer to his flag in such a situation that one captain will always chase between E1 and E2 and the other one in alternance will always chase between F2 and G2. ANd if he first plays his captain I4 you can move your miner forward from E6 but never bring it to E1 otherwise you will get trapped and he can capture it with the other captain without leaving you enough moves to bring your second miner from J5 close enough from the flag. So also in this case you will be forced to move backwards and he will have all time to bring his 2 captains to chase alternatively E1/E2 and F2/G2.
So in this case, if red starts, the outcome can only be a draw, so my opponent did a wrong decision to disconnect and give me the victory.
2) If blue has to play the outcome of the game is a victory for blue. Let's explain: first you move your miner from E6 straight forward to E1. If he moves his captain from A3 he will not be able to capture your miner so you have a free path to the flag. So he is obliged to move his captain from I4. By doing so at one time you will have your miner in E1 and he will have his captain in F2. and it will be your turn to play. At this stage his captain in F2 cannot move without giving you free access to the flag. So you now have enough moves available to bring your miner from J5 to H2 while in the meanwhile he will bring his captain from A3 to E3 and it is his turn to play. If he moves his captain out of F2 your miner in E1 has a free path to the flag, if he moves his other captain from E3 to E2 or to F3 you move your miner from E1 to capture bomb in F1, he is then obliged to capture this miner, so you move your other miner from H2 to G2 and then to G1 and capture the flag
3) There are several possibilities to place the 3 blue miners and the 2 red captains in such a way that it is a clear victory for red. for example blue miners are in J2; J5 and J7 and red captains are in I4 and I6. Red moves captain from E6 to E5 and next move capture miner in J5, same captain continues straight forward to capture miner in J2. While blue may move his miner from J7 to F7. Once this miner is in F7 red brings his captain from I4 to F4 and blocks the path in the middle to this last miner. blue has to move backwards and red has all possibilities then to bring his other captain in the middle zone and with 2 captains against 1 miner red can only win.
This example shows that not only the remaining forces on each side are determinant for the outcome of a game. In the above example with 3 miners against 2 captains the outcome of the game can be a victory for the miners, a victory for the captains or a draw. It all depends from where the pieces are located at the beginning of the action and whose turn it is to play.
- Mitthunder likes this
Posted 28 February 2014 - 07:55 PM
Hey, Napoleon 1er, I've been puzzling over this for awhile today. I can't quite see my way through to it, but it does look like the key to blue winning--if it is possible--when red goes first might be that when the red captain at A3 breaks the 2 square advantage over the blue Miner in A6 by moving to B3 (as you begin with), then blue must immediately move his A-File Miner up the A-File toward the A1 corner in the very next move. This A-File Miner is now a bigger problem for the red Captain because now the Captain does not have 2 square advantage on the blue Miner. I've worked out a variety of ways in which I can see blue winning here but I'm not perfectly sure I'm playing red in the ideal way just yet to preserve the draw.
In all the ways I have blue winning in this situation (when red moves first) they begin with the same A3 red Captain that you do and generally just force the red Captain to fight as spread-out as possible a two-front war with the Miners. The A-File Miner proceeds to the A1 corner with the goal of the biggest spread he can get, and then blue works it down from there.
Napoleon 1er, can you see any unstoppable blue plan of success with this plan of attack in mind against red?
The complete GS&F Rules can be found here: http://forum.strateg...rum-rules-2016/
Draw Refusal Rules, specifically, can be read here: http://forum.strateg...604#entry339604
Posted 28 February 2014 - 09:38 PM
If red starts with his captain in I4 and goes to F2 it maybe easier to see the draw. The goal of red should be to bring one captain to chase in F2 and G2 and the other in E1 and E2. Blue will always be one move behind.
Posted 28 February 2014 - 11:03 PM
Answer to Quizz number 2 by Napoleon 1er - 2 square rule is active over long distance and above the lakes
1) moving your miner from E9 to E8 is a fatal error because red will capture it with his major from F8 to E8 and leave you with one single piece on the board which makes you vulnerable in a 2 square battle. Furthermore at this stage of the game the major is no more a threat for you (neither for your colonel (obvious) nor for your flag (behind bombs) so capturing the major at this point is purely honorific and doesn't provide you any additional advantage. The only real threat for you is the red miner. Let's analyze the various options:
option a: If you capture the major with your colonel from D8, red can move his miner from D1 to C1 and you have no more possibility to get the 2 square rules acting in your favor. WHatever you do to bring back your colonel red can play it as he wants moving first to corner left in A1. At this point your colonel will have reached maximum C8 and it is your turn to move. So you move C8 to B8, red moves miner from A1 to A2. If you then move your colonel from B8 to A8 red miner plays the 2 square rule in his favor and you are the player who has to stop the 2square chasing first (3 moves max), then you have to move your colonel vertically. Doing so red miner moves one step downwards to A3 ... and so on until miner reaches corner A10 where the same 2square rules will always be in his favor, so he can turn right and move to the flag. You will always be caught by this 2 square rule.
option b: move your colonel in C8, red moves his miner from D1 to D2, then if you move back to D8 he moves miner to C2 and you are again the starter of the 2square chasing (even over the lakes and over long distance) so you will not be allowed to come back on C8 so he will profit from the opportunity to move from C2 to B2 and will find himself again in the same situation as option a beeing 2 columns ahead of you. His next move is B2 to A2 and then same game end as option a will happen
option c: move your colonel from D8 to D7, red moves his miner from D1 to D2, then if you move your colonel to E7 he moves his miner to C2 and is again with 2 columns ahead of you, so red can just continue to A2 and then same game end happens as option b. If you move your colonel from D7 to C7 red will move the miner from D2 to E2 and is also 2 columns ahead of you so he can continue until F2 and then play the same as if he would be in column A (by symmetry). The 2square rule will always be in his favor (at one point he will only have to move back his major (to G8) from the path of his miner if you didn't capture it while moving back from C7) and the same game end will happen as in option a or b but with the miner approach in column F instead of column A. Last option for you was to move back your colonel from D7 to D8 instead of moving it right or left. Again in this case you will get caught by the 2 square rules because while the red miner can move back and forth between D2 and D4 as much as he want you are limited to 3 moves between D7 and D8 because you do not have the possibility to make a third move on D9 because occupied by your bomb, so at one point you have to move right or left which gives him the path to the flag by moving his miner in the opposite direction as described in option c above.
Here comes the lesson from this quizz: Never let your opponent leave you with one single piece on the board (as strong as this piece might be) while he still has a miner, because he will always win. There is one little exception to this principle in case there are no bomb on row 9: to simplify the explanation imagine that in the quizz 2 red would be left with only his miner in D1 (no scout and no major) while blue is left only with his colonel in D8 and bomb in D9 has been removed, all other bombs and flag remain unchanged. In this situation it is a draw because blue can move back and forth between D7 and D9 as long as red moves back and forth between D2 and D4. So blue, to obtain the draw, shall just continuously follow the red miner in such a way to always remain in the same column than him, so red will never find a solution to get the 2 square rules in his favor
2) so what should have been the right move instead of moving the blue miner from E9 to E8? Many have found the right answer. Move colonel from D8 to D7 then E7 and F7. Then the following can happen:
option a: If red moves his major from F8 to E8 you move your miner to F9 and then G9, G8 and you can go searching his flag from the right with your miner. If he plays correctly he is obliged to bring his red miner in the same zone than yours until the miner exchange occurs, ending the game in a draw.
option b: If red moves his major from F8 to G8 or to F9, you move your miner from E9 to E8 then D8 and you can go searching his flag from the left. If he plays correctly he is obliged to cut the path of your miner with his miner so the game ends also in a draw.
I have not found a solution for ending with a victory for blue but I do not exclude it could be possible. If anybody has a solution please post it here
Posted 01 March 2014 - 04:14 AM
Thank you Napoleon, for your answers to these interesting problems; I have learned a lot! However, I believe that your answer to Quiz #2 is not fully correct. If blue makes the fatal mistake and has his colonel at E8, with the red miner at D1 and it being red's turn to move, the red miner will not be able to gain the 2-squares advantage without taking one turn to move his scout sometime after the miner makes it to A1, though red will still surely win the game.
Now, if red had only the miner at D1 and no scout, with the blue colonel at E8 and it is red's turn to play, then the miner will be unable get into a favorable 2-squares position and it will be a draw. The key is not what columns the two pieces are in at the beginning of the sequence but rather whether the number of spaces between them is even or odd. The miner can win only if the number of spaces is an odd number when it is his turn to move. Since D1 to E8 is 8 spaces, the best the miner could do is a draw.
You correctly pointed out that if the power piece has three spaces to move vertically in all columns then it can stop the miner and it will be a draw (in this case odd or even doesn't matter). Also, if both players have a bomb in their 2nd row from the back in the same column, then high piece is also able to stay lined up with the miner. Even if the miner has a companion to help it, the high piece could still get the draw in either of these situations. It would just need to ignore the companion and move vertically always staying in the same column as the miner.
Posted 01 March 2014 - 11:24 AM
Thanks for your remarks which are well appreciated, I recognize it is correct that in 50% of the cases (when number of spaces between the pieces is even) in order to ensure 100% victory red has to make 1 move with his scout.
... finally the scout is still necessary, my instinct told me it was but I couldn't figure it out, thanks again.
Posted 12 March 2015 - 10:40 PM
Answer to Quizz number 3 by Napoleon 1er - The power against the quantity
YOur next move shall be miner from F5 to F4. If you don't do that he will move his captain from E3 to E4 and then approach with his lieutnant from I7 to capture it. Having a miner inside his field gives you a completely different advantage. You will be driving the game and oblige him to do what you want. Let's analyze his possibilities after you move your miner in F4:
1) If he moves captain from E3 to E4 you move your miner to G4!!!, if he pursues you with the captain you move to G3, then if he continues pursuing you with the captain continue moving towards his flag (note that he cannot move his m from E2 to F2 or to E1 because otherwise you can go to C1 with your scout from B10 in 2 moves), if he moves his colonel from D4 to D3 start approaching your colonel as well via column B. Then continue approaching your colonel until you can pass your miner from A7 to A1 behind your colonel. This will oblige him to bring his captain back in that area in diagonal of your miner and make the colonel exchange or let you bring your colonel on C1. If he moves his m from J2 to I2, move your miner from G3 to row 1. At this stage you may have a miner in A3 with his captain unmovable in B2, a miner in G1 and a scout in J4 for a m in D2 and a m in H2 .... if you move your miner from G1 to D1 you can sacrify it to the m and open the path for your scout or your other miner ....
2) If he moves his colonel from D4 to E4 and pursue your miner let him capture it on G3 ... this will give you full time to bring your colonel on C1 via column B
3) if he makes any other move for example threatening your scout in J4 with his m moving from J2 to J3 just let him capture it .... he is only moving further from the battle zone and the number of total moves towards his flag is in your favour.
4) If he moves his m from E2 to D2, start approaching your colonel and your A7 miner on the left side
Posted 12 March 2015 - 10:43 PM
Answer to Quizz number 4 by Napoleon 1er - No piece is as strong as a bomb to protect the flag
ANswer from Astros is correct. Bring one of your pieces in diagonal of his colonel. Because he will not be allowed to endlessly chase you he will be obliged to make a non chasing move after 5 moves which will give you access to the flag.
Posted 12 March 2015 - 11:21 PM
Answer to Quizz number 5 by Napoleon 1er - Single scout versus 3 major pieces is not always a draw
To kill this last scout with 3 pieces you need here to proceed with method. Do not try to get it in just a few moves you will just not be successful. First thing is to divide the board in 4 square zones as follows:
Zone 1: square made by joining the cells F1 - J1 - J5 - F5
Zone 2: square made by joining the cells J6 - J10 - F10 - F6
Zone 3: square made by joining the cells E6 - E10 - A10 - A6
Zone 4: square made by joining the cells A5 - A1 - E1 - E5
so we can see that there are bombs and flags in zones 1; 3 and 4 while zone 2 is empty .... so one can understand that in this zone 2 the scout is more comfortable to move freely while in the other zones it is more difficult for him to escape. SO the method to apply is to either trap the scout in one of the 4 zones or push him out of it without leaving him possibility to come back in a zone from which he has been thrown out. So first move your 3 pieces as shown on picture below without thinking to capture the scout, just concentrate on placing your pieces:
In this situation if the scout would be in zone 1 he would be trapped and could be easily captured by moving major and lieutnant upwards. If he is not there don't let him the possibility to come back in zone 1. So if he is in column J just move down your lieutnant to force him moving out of column J. Once he is out of column J move your lieutnant to F8. At this moment watch where his scout is.
1) If he is out of zone 2 just move your major from I7 to H7 so he will not be able to come back to zone 2. Then move your major and your lieutnant horizontally to the left in alternance. if he moves from zone 3 to row 3 in zone 4, move your captain from E4 to E3, the 2 square rule will always be in your favour and this will disable for him the possibility to come back in zone 2 through the center. If he moves from zone 3 to row 4 in zone 4 just let him do and continue moving your major and lieutnant in parallel to the left. At a certain point he will also not be more in degree to come back to zone 3 and you can trap him in zone 4
2) If he is still in zone 2 at this moment you can see that with your major in I7 and lieutnant in F8 he is trapped in zone 2. If he moves to column J you close him the path to zone 1 by moving your major to J7, if he tries to escape through G7 or E9, your lieutnant is there to block him with a 2square rule. If he makes any other move not in column J, G7 or E9 you can start moving down your captain to zone 2 G9 and from there you can trap him.
if he is not very sportsmanlike he could try to make endless moves between E9; G9; G7 and J9 just to not let you bring your captain in zone 2. If you have such opponent you can still win if you let him escape to zone 3 from G7 and then close the return to zone 2 by moving your major to H7. Then proceed as per 1) above.
There are certainly other possibilities to kill the scout starting from another zone than zone 1 but let you the pleasure to find them. Important is the method and thinking to position correctly your pieces before trying to capture him.
Posted 22 March 2015 - 09:10 AM
Answer to Quizz number 6 by Napoleon 1er - passing miners
First bring miner from I9 to H7, then move down your colonel from I6 to I7. If he brings his captain from E5 to G7 just move up your miner from E10 to E8, He will be obliged to bring back his captain from G7 to the center to block the passing of your miner in E8. So you move your colonel to I8 and then move your miner from H7 to I7 and I6 and I5. He will be obliged to capture it with his lieutnant but your colonel will then be in the same column and can move up to push out the lieutnant from columns I and J due to 2square rule. He will be obliged to retreat to H4 when your colonel will be in I3. Then you have a full free path for your miner in J1 to move the the flag in G1.
Posted 22 March 2015 - 09:31 AM
Answer to Quizz number 7 by Napoleon 1er - How to break a double chase
Both solutions have been given already. In fact I did not think to solution to bring miner G8 to I10 but did exactly what Desert Oasis said (and which is the only solution in case your 3rd miner is in A1 (Quizz N°7 bis)). What you have to do to break the double chase is forcing him to make a vertical move elsewhere than in column J cause in column J your miner would be blocked by your own lieutnant in J2. So bring your miner from I4 to A4, let him capture your lieutnant in B3 and then he will be forced to move his captain vertically either from B3 to B4 or from F7 to F8. Once he moves captain from B3 to B4, take the bomb in A3 and use the bomb in B2 to disable him threatening your miner. This will give you 1 free move every 4 moves so you can start approaching your miner from A1 and with 3 miners against 2 captains you get easily to the flag.
Posted 12 July 2015 - 05:27 PM
Answer to Quizz number 8 by Napoleon 1er - How to trap that last scout
For that case you (playing as Edwinvandebraak) have to make your moves systematically applying the following principles:
1) First of all bring your 4 major pieces on the 4 cells D8, F7, I7 and J9 as shown on the initial situation board below for both 8a and 8b without preoccupying what the opponent does with the scout. Once you have done this observe where the scout is. If he is below the lakes then proceed as for case 8a below, otherwise proceed as for 8b. On the board below, for clarity purpose, I have identified in white all cells that the scout could reach within one or two moves. To trap the scout you need only need to proceed systematically focusing on reducing the white zone. After you have reached a certain positioning you get a clear win situation. See detailed explanations below.
case 8a: http://imgur.com/uP9jl0M
case 8b: http://imgur.com/x818mek
2) At any time while you are trying to trap the scout if the opponent moves any other piece just stop trapping the scout and go get capturing the piece that has moved by taking it in sandwich with 2 of your major pieces. Then come back to scout trapping.
3) At any time during trapping the scout your captain in D8 is guarding your flag. So as soon he would try to pass a piece from the left this captain is close enough from that path to block it.
4) Accept that to reach the clear win situation may take you a lot of time, certainly more than 10 minutes.
Detailed explanation case 8a:
Once you have placed your 4 major pieces in the initial position the scout must be on one of the white cell. Following principles apply then: a) if at any time he would move from b8 to a8 your immediate following move shall be major from f7 to e7 (this will give you advantage for the 2square rule afterwards). If he comes back to B8 move back your major to F7. if he moves then up from a8 go to case 8b. b ) If at any time he would move his scout on either e9 or e10 coming from left (= from cells b9, c9, c10 or d10) then close him the path to the othe side of the lakes by moving your captain from d8 to e8. If he would move his scout to either e9 or e10 coming from right (= from cells f9,g9, h9,f10, g10, h10, i10 or j10) then close him the path to the other side of the lakes by moving your major from f7 to e7. By doing this you will always have the 2square rule in your favor and he will be the first one having to make a different move. So he cannot escape through the middle. c) if he is making any other move than those described above just bring your lieutnant from j9 to h9. During this operation if he brings his scout to j10 or j8 close him the path to other side of the lake by moving your captain from i7 to j7 (2 square rule in your favor). Once your are in h9 with your lieutnant watch what he moved. He has a suicide cell in J9 (in case he would be moving from J10 to j9 after your captain made i7 to j7) and a dead end cell in g8 (if he goes there from g10 just bring your lieutnant from h9 to h8, 2square rule in your favor. If the scout has made any other move except those particular case described above (move from b8 to a8, to e9, e10, j8 or j10) for which your response is also described above, then start to move down your captain from i7 to i10. At this moment you have reached a clear win situation, only move your lieutnant from h9 and your captain from i10 horizontally to the left and you get trap it. If he is on b9 bring your other captain from d8 to d7. White zone has reduced to zero left cells, scout is trapped.
Detail explanation for case 8b:
Once you have placed your 4 major pieces in the initial position the scout must be on one of the white cell. Following principles apply then: a) if at any time he would move the scout from somewhere in column a to a8, then move your captain from d8 to c8 to block him access to lower gamefield. b ) if at any time he would move to e3 or e4 coming from left close him the path to below the lakes by moving your captain from d8 to e8. If at any time he would move to e3 or e4 coming from right close him the path to below the lakes by moving your major from f7 to e7. c) let him do any other move in the white zone and move up your major from f7, captain from i7 and lieutnant from j9 as shown on intermediate situation 8b 1 then to intermediate situation 8b 2. At this stage white zone is already reduced and he has 2 suicide cells. If he moves to g4 move up your major to f4 and then he is trapped in a 2square rule. even if he moves to j3 your captain in i4 will block him the path to below the lakes and j2 is the 2nd suicide cell. d) if does any other move except those particular described above then move your lieutnant from h2 to g2 and then g3. If at that time he is in h2 or f2 bring your major up to f4 and the scout is trapped on the left. If he is on the right you have now both your lieutnant in h3 or g3 and captain in i4 that can go marching parallel horizontally to the left and trap him there. your captain from d8 to c8 always blocking the path downwards on left.
- The Prof likes this
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