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
how to parse json to list?
Is there any reason nowadays to use a neon indicator lamp instead of a LED?
Escape the labyrinth!
Nanomachines *exists* Axolotl-levels of regeneration *exists* So how the hell can crippling injuries exist as well?
Persuading players to be less attached to a pre-session 0 character concept
Why are there two bearded faces wearing red hats on my stealth bomber icon?
Delete empty subfolders, keep parent folder
The relationship of noch nicht and the passive voice
Is it possible to get a pointer to one subobject via a pointer to a different, unreleated subobject?
Debussy as term for bathroom?
Who are the people reviewing far more papers than they're submitting for review?
Do household ovens ventilate heat to the outdoors?
Specifying BOM substitutions / alternatives with Contract Manufacturer (CM)
How should I avoid someone patenting technology in my paper/poster?
rule-based deletions from string list
I was cheated into a job and want to leave ASAP, what do I tell my interviewers?
Manager manipulates my leaves, what's in it for him?
How does one calculate the distribution of the Matt Colville way of rolling stats?
Is Zack Morris's 'time stop' ability in "Saved By the Bell" a supernatural ability?
Is the Necromancer's "Half-Formed Golem" pet available for all classes?
Temporarily moving a SQL Server 2016 database to SQL Server 2017 and then moving back. Is it possible?
Lead Amalgam as a Material for a Sword
Do you add your strength modifier once or twice to an unarmed strike?
What are the end bytes of *.docx file format
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;
$begingroup$
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
New contributor
$endgroup$
add a comment
|
$begingroup$
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
New contributor
$endgroup$
$begingroup$
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
|
$begingroup$
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
New contributor
$endgroup$
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
New contributor
New contributor
New contributor
asked 8 hours ago
John FoleyJohn Foley
311 bronze badge
311 bronze badge
New contributor
New contributor
$begingroup$
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
add a comment
|
1 Answer
1
active
oldest
votes
$begingroup$
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.
$endgroup$
add a comment
|
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "559"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/4.0/"u003ecc by-sa 4.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
John Foley is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f89241%2fthe-100-soldier-problem%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
$endgroup$
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.
$endgroup$
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.
$endgroup$
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.
edited 7 hours ago
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
|
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.
Thanks for contributing an answer to Puzzling Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f89241%2fthe-100-soldier-problem%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Related: fivethirtyeight.com/features/can-you-rule-riddler-nation (The riddler classic)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago