The 100 soldier problemA 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
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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
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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
asked 8 hours ago
John FoleyJohn Foley
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$begingroup$
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?
mathematics game
asked 8 hours ago
John FoleyJohn Foley
311 bronze badge
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
add a comment
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$begingroup$
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?
mathematics game
asked 8 hours ago
John FoleyJohn Foley
311 bronze badge
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
mathematics game
asked 8 hours ago
John FoleyJohn Foley
311 bronze badge
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
311 bronze badge
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
311 bronze badge
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
311 bronze badge
asked 8 hours ago
John FoleyJohn Foley
311 bronze badge
311 bronze badge
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
add a comment
|
$begingroup$
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
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1 Answer
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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.
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
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$begingroup$
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.
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
$endgroup$
add a comment
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$begingroup$
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.
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
$endgroup$
add a comment
|
$begingroup$
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.
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
$endgroup$
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.
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
edited 7 hours ago
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
answered 7 hours ago
Dr XorileDr Xorile
15.3k3 gold badges34 silver badges96 bronze badges
15.3k3 gold badges34 silver badges96 bronze badges
add a comment
|
add a comment
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John Foley is a new contributor. Be nice, and check out our Code of Conduct.
John Foley is a new contributor. Be nice, and check out our Code of Conduct.
John Foley is a new contributor. Be nice, and check out our Code of Conduct.
John Foley is a new contributor. Be nice, and check out our Code of Conduct.
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Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
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– im_so_meta_even_this_acronym
5 hours ago