Two armies in the field












0














Assume two armies of unequal size are fighting, where each soldier on both sides is of equal ability.



Assume that each soldier is capable of taking out an enemy soldier each [unit of time], and that the battle continues until one side is annihilated.



How would you determine the size of the surviving army?



There are no volleys, or distinct actions by either army -- consider a "fire at will" scenario.



That is, how would you determine how many soldiers would a larger army have left after the lesser army is annihilated, all things being equal, and knowing only the size of each army?










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  • 1




    Subtract? If one army has 100, and the other has 75, then larger army should be left with 25...
    – Arturo Magidin
    Dec 3 '18 at 20:34
















0














Assume two armies of unequal size are fighting, where each soldier on both sides is of equal ability.



Assume that each soldier is capable of taking out an enemy soldier each [unit of time], and that the battle continues until one side is annihilated.



How would you determine the size of the surviving army?



There are no volleys, or distinct actions by either army -- consider a "fire at will" scenario.



That is, how would you determine how many soldiers would a larger army have left after the lesser army is annihilated, all things being equal, and knowing only the size of each army?










share|cite|improve this question


















  • 1




    Subtract? If one army has 100, and the other has 75, then larger army should be left with 25...
    – Arturo Magidin
    Dec 3 '18 at 20:34














0












0








0







Assume two armies of unequal size are fighting, where each soldier on both sides is of equal ability.



Assume that each soldier is capable of taking out an enemy soldier each [unit of time], and that the battle continues until one side is annihilated.



How would you determine the size of the surviving army?



There are no volleys, or distinct actions by either army -- consider a "fire at will" scenario.



That is, how would you determine how many soldiers would a larger army have left after the lesser army is annihilated, all things being equal, and knowing only the size of each army?










share|cite|improve this question













Assume two armies of unequal size are fighting, where each soldier on both sides is of equal ability.



Assume that each soldier is capable of taking out an enemy soldier each [unit of time], and that the battle continues until one side is annihilated.



How would you determine the size of the surviving army?



There are no volleys, or distinct actions by either army -- consider a "fire at will" scenario.



That is, how would you determine how many soldiers would a larger army have left after the lesser army is annihilated, all things being equal, and knowing only the size of each army?







algebra-precalculus






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asked Dec 3 '18 at 20:30









ridthyself

1346




1346








  • 1




    Subtract? If one army has 100, and the other has 75, then larger army should be left with 25...
    – Arturo Magidin
    Dec 3 '18 at 20:34














  • 1




    Subtract? If one army has 100, and the other has 75, then larger army should be left with 25...
    – Arturo Magidin
    Dec 3 '18 at 20:34








1




1




Subtract? If one army has 100, and the other has 75, then larger army should be left with 25...
– Arturo Magidin
Dec 3 '18 at 20:34




Subtract? If one army has 100, and the other has 75, then larger army should be left with 25...
– Arturo Magidin
Dec 3 '18 at 20:34










1 Answer
1






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oldest

votes


















2














You appear to be describing a situation modeled by Lanchaster's linear law, where the result is the larger force has the difference in numbers surviving. With firearms, this corresponds to the results of unaimed fire.



You should also be aware of Lanchester's square law, which applies when there is aimed fire.



In modern warfare, there is usually a mix of aimed and unaimed fire, so powers between $1$ and $2$ can be more accurate.






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  • Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
    – ridthyself
    Dec 4 '18 at 12:37











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1 Answer
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active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

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active

oldest

votes









2














You appear to be describing a situation modeled by Lanchaster's linear law, where the result is the larger force has the difference in numbers surviving. With firearms, this corresponds to the results of unaimed fire.



You should also be aware of Lanchester's square law, which applies when there is aimed fire.



In modern warfare, there is usually a mix of aimed and unaimed fire, so powers between $1$ and $2$ can be more accurate.






share|cite|improve this answer





















  • Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
    – ridthyself
    Dec 4 '18 at 12:37
















2














You appear to be describing a situation modeled by Lanchaster's linear law, where the result is the larger force has the difference in numbers surviving. With firearms, this corresponds to the results of unaimed fire.



You should also be aware of Lanchester's square law, which applies when there is aimed fire.



In modern warfare, there is usually a mix of aimed and unaimed fire, so powers between $1$ and $2$ can be more accurate.






share|cite|improve this answer





















  • Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
    – ridthyself
    Dec 4 '18 at 12:37














2












2








2






You appear to be describing a situation modeled by Lanchaster's linear law, where the result is the larger force has the difference in numbers surviving. With firearms, this corresponds to the results of unaimed fire.



You should also be aware of Lanchester's square law, which applies when there is aimed fire.



In modern warfare, there is usually a mix of aimed and unaimed fire, so powers between $1$ and $2$ can be more accurate.






share|cite|improve this answer












You appear to be describing a situation modeled by Lanchaster's linear law, where the result is the larger force has the difference in numbers surviving. With firearms, this corresponds to the results of unaimed fire.



You should also be aware of Lanchester's square law, which applies when there is aimed fire.



In modern warfare, there is usually a mix of aimed and unaimed fire, so powers between $1$ and $2$ can be more accurate.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 3 '18 at 20:41









Eric Towers

31.9k22265




31.9k22265












  • Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
    – ridthyself
    Dec 4 '18 at 12:37


















  • Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
    – ridthyself
    Dec 4 '18 at 12:37
















Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
– ridthyself
Dec 4 '18 at 12:37




Lancaster's square law is what I was looking for, specifically, to find the size of the surviving army, you use sqrt(L^2 - S^2), where L is the larger army's size and S is the smaller.
– ridthyself
Dec 4 '18 at 12:37


















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