2 player nim game

1,728
13
Hi all, ok there are 3 piles containing objects; Pile A, Pile B and Pile C.

Let the Nim-sum of all 3 piles be denoted as X.

Let Pile A and Pile B and Pile C contain objects.
( In Nim-Sum )

A + X = D

B + X = E

C + X = F

As we are currently in research of a math project, we are wondering if there is a case whereby D > A, E > B, and F > C. If not, what is the proof?
 

HallsofIvy

Science Advisor
Homework Helper
41,728
881
Perhaps I am not understanding the question. The number of objects in each pile are A, B, C respectively. What do you mean by "Nim-sum"? Certainly if X> 0 then it must be the case that D> A, E> B, and F> C.
 

CRGreathouse

Science Advisor
Homework Helper
2,817
0
Hi all, ok there are 3 piles containing objects; Pile A, Pile B and Pile C.

Let the Nim-sum of all 3 piles be denoted as X.

Let Pile A and Pile B and Pile C contain objects.
( In Nim-Sum )

A + X = D

B + X = E

C + X = F

As we are currently in research of a math project, we are wondering if there is a case whereby D > A, E > B, and F > C. If not, what is the proof?
I don't know what a Nim-Sum is, but from what you have
[tex]D>A\Leftrightarrow E>B\Leftrightarrow F>C\Leftrightarrow X>0[/tex]

so you're just asking if the Nim-Sum is always negative. Well, define it for us and we'll see!
 
Last edited:
1,424
1
According to wikipedia, a nim-sum is an operation used in game theory.
 

Related Threads for: 2 player nim game

Replies
2
Views
3K
  • Last Post
Replies
4
Views
693
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
2
Replies
26
Views
1K
Replies
6
Views
1K

Hot Threads

Top