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The 100 soldier problem


A Strategy Game Involving Conquering of RegionsWhat size of puzzle is appropriate?Fastest way to collect an arbitrary armyAt the Parking LotThe Fanatic Fever(twist on the 5 pirates puzzle)Monte Carlo ChessA dark and stormy Car Talk quibblerCheating aplenty at Build-a-Die 2017A Strategy Game Involving Conquering of RegionsHow many nodes in the network?Another variation of the game of Nim






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








6












$begingroup$


I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of Regions



Wellington and Napolean each have an army of 100 soldiers. Each army is divided into 10 platoons. A platoon can have any number of soldiers. When the action begins, Platoon 1 from Wellington's army engages with Platoon 1 from Napoleon's army, Platoon 2 engages with its opposite number and so on. The platoon having more soldiers than the opposition wins their individual engagement.



If you were one of the generals, how would you distribute your soldiers so as to have the maximum chance of (a) winning the most platoon engagements and (b) defeating the greatest number of opposition soldiers?










share|improve this question







New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$













  • $begingroup$
    Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
    $endgroup$
    – im_so_meta_even_this_acronym
    5 hours ago

















6












$begingroup$


I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of Regions



Wellington and Napolean each have an army of 100 soldiers. Each army is divided into 10 platoons. A platoon can have any number of soldiers. When the action begins, Platoon 1 from Wellington's army engages with Platoon 1 from Napoleon's army, Platoon 2 engages with its opposite number and so on. The platoon having more soldiers than the opposition wins their individual engagement.



If you were one of the generals, how would you distribute your soldiers so as to have the maximum chance of (a) winning the most platoon engagements and (b) defeating the greatest number of opposition soldiers?










share|improve this question







New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$













  • $begingroup$
    Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
    $endgroup$
    – im_so_meta_even_this_acronym
    5 hours ago













6












6








6


1



$begingroup$


I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of Regions



Wellington and Napolean each have an army of 100 soldiers. Each army is divided into 10 platoons. A platoon can have any number of soldiers. When the action begins, Platoon 1 from Wellington's army engages with Platoon 1 from Napoleon's army, Platoon 2 engages with its opposite number and so on. The platoon having more soldiers than the opposition wins their individual engagement.



If you were one of the generals, how would you distribute your soldiers so as to have the maximum chance of (a) winning the most platoon engagements and (b) defeating the greatest number of opposition soldiers?










share|improve this question







New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$




I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of Regions



Wellington and Napolean each have an army of 100 soldiers. Each army is divided into 10 platoons. A platoon can have any number of soldiers. When the action begins, Platoon 1 from Wellington's army engages with Platoon 1 from Napoleon's army, Platoon 2 engages with its opposite number and so on. The platoon having more soldiers than the opposition wins their individual engagement.



If you were one of the generals, how would you distribute your soldiers so as to have the maximum chance of (a) winning the most platoon engagements and (b) defeating the greatest number of opposition soldiers?







mathematics game






share|improve this question







New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.










share|improve this question







New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








share|improve this question




share|improve this question






New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








asked 8 hours ago









John FoleyJohn Foley

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New contributor



John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




New contributor




John Foley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • $begingroup$
    Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
    $endgroup$
    – im_so_meta_even_this_acronym
    5 hours ago
















  • $begingroup$
    Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
    $endgroup$
    – im_so_meta_even_this_acronym
    5 hours ago















$begingroup$
Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago




$begingroup$
Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago










1 Answer
1






active

oldest

votes


















3














$begingroup$

I'll kick off with some observations.




I think there is no winning strategy. The game as envisaged is mind-blowing because there are 4,263,421,511,271 possible ways of arranging your army. However, suppose that there were a configuration that maximized either a or b. Then both sides would use it and all 10 platoons would be a draw.


But, if you knew what your opposition were going to do, then you'd just mirror their army, take the smallest platoon with size $geq 9$, and give 1 to each other army winning 9 battles.


Then again, it would depend on what your opponent's objectives were. If he simply wanted to save as many men as possible, he'd do something like $(100,0,0,ldots)$. Easy to beat with objective (a) and impossible with objective (b). So it is important to know whether the opposing general knows about your objective and/or has an objective of their own.


But ultimately this reduces to something like rock, paper, scissors. There may be a best strategy if you're playing multiple games, but with one game there's no solution.


That all said, there may be something whereby you should pick from a set of possible answers, or perhaps eliminate certain choices depending on your objective.




I'll be interested to see what other people come up with.






share|improve this answer











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    1 Answer
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    1 Answer
    1






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    active

    oldest

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    active

    oldest

    votes









    3














    $begingroup$

    I'll kick off with some observations.




    I think there is no winning strategy. The game as envisaged is mind-blowing because there are 4,263,421,511,271 possible ways of arranging your army. However, suppose that there were a configuration that maximized either a or b. Then both sides would use it and all 10 platoons would be a draw.


    But, if you knew what your opposition were going to do, then you'd just mirror their army, take the smallest platoon with size $geq 9$, and give 1 to each other army winning 9 battles.


    Then again, it would depend on what your opponent's objectives were. If he simply wanted to save as many men as possible, he'd do something like $(100,0,0,ldots)$. Easy to beat with objective (a) and impossible with objective (b). So it is important to know whether the opposing general knows about your objective and/or has an objective of their own.


    But ultimately this reduces to something like rock, paper, scissors. There may be a best strategy if you're playing multiple games, but with one game there's no solution.


    That all said, there may be something whereby you should pick from a set of possible answers, or perhaps eliminate certain choices depending on your objective.




    I'll be interested to see what other people come up with.






    share|improve this answer











    $endgroup$



















      3














      $begingroup$

      I'll kick off with some observations.




      I think there is no winning strategy. The game as envisaged is mind-blowing because there are 4,263,421,511,271 possible ways of arranging your army. However, suppose that there were a configuration that maximized either a or b. Then both sides would use it and all 10 platoons would be a draw.


      But, if you knew what your opposition were going to do, then you'd just mirror their army, take the smallest platoon with size $geq 9$, and give 1 to each other army winning 9 battles.


      Then again, it would depend on what your opponent's objectives were. If he simply wanted to save as many men as possible, he'd do something like $(100,0,0,ldots)$. Easy to beat with objective (a) and impossible with objective (b). So it is important to know whether the opposing general knows about your objective and/or has an objective of their own.


      But ultimately this reduces to something like rock, paper, scissors. There may be a best strategy if you're playing multiple games, but with one game there's no solution.


      That all said, there may be something whereby you should pick from a set of possible answers, or perhaps eliminate certain choices depending on your objective.




      I'll be interested to see what other people come up with.






      share|improve this answer











      $endgroup$

















        3














        3










        3







        $begingroup$

        I'll kick off with some observations.




        I think there is no winning strategy. The game as envisaged is mind-blowing because there are 4,263,421,511,271 possible ways of arranging your army. However, suppose that there were a configuration that maximized either a or b. Then both sides would use it and all 10 platoons would be a draw.


        But, if you knew what your opposition were going to do, then you'd just mirror their army, take the smallest platoon with size $geq 9$, and give 1 to each other army winning 9 battles.


        Then again, it would depend on what your opponent's objectives were. If he simply wanted to save as many men as possible, he'd do something like $(100,0,0,ldots)$. Easy to beat with objective (a) and impossible with objective (b). So it is important to know whether the opposing general knows about your objective and/or has an objective of their own.


        But ultimately this reduces to something like rock, paper, scissors. There may be a best strategy if you're playing multiple games, but with one game there's no solution.


        That all said, there may be something whereby you should pick from a set of possible answers, or perhaps eliminate certain choices depending on your objective.




        I'll be interested to see what other people come up with.






        share|improve this answer











        $endgroup$



        I'll kick off with some observations.




        I think there is no winning strategy. The game as envisaged is mind-blowing because there are 4,263,421,511,271 possible ways of arranging your army. However, suppose that there were a configuration that maximized either a or b. Then both sides would use it and all 10 platoons would be a draw.


        But, if you knew what your opposition were going to do, then you'd just mirror their army, take the smallest platoon with size $geq 9$, and give 1 to each other army winning 9 battles.


        Then again, it would depend on what your opponent's objectives were. If he simply wanted to save as many men as possible, he'd do something like $(100,0,0,ldots)$. Easy to beat with objective (a) and impossible with objective (b). So it is important to know whether the opposing general knows about your objective and/or has an objective of their own.


        But ultimately this reduces to something like rock, paper, scissors. There may be a best strategy if you're playing multiple games, but with one game there's no solution.


        That all said, there may be something whereby you should pick from a set of possible answers, or perhaps eliminate certain choices depending on your objective.




        I'll be interested to see what other people come up with.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 7 hours ago

























        answered 7 hours ago









        Dr XorileDr Xorile

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