10165 - Stone Game

All about problems in Volume 101. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

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10165 - Stone Game

Post by 10153EN »

Dear all,

I still have no idea on how to solve this problem after thinking over it for some time. Could anyone give me some hint on it?


Stefan Pochmann
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Post by Stefan Pochmann »

It's the "Nim" game and you should easily find information in google when you search for "nim" and "xor", for example here:


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10165 - Stone Game

Post by konsept »

Can someone explain the solution to this problem ?
it looks similar to the NIM-game.

Thank you.

Shih-Chia Cheng
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Re: 10165 - Stone Game

Post by Shih-Chia Cheng »

konsept wrote:Hi,
Can someone explain the solution to this problem ?
it looks similar to the NIM-game.

Thank you.
Convert all numbers into binary sequences and list them all one in a row.
Then you may think what the best strategy is for playing the game.
If this is still obscure, consider the special case when there are only two
piles of stones. Try to generalize your solution for this special case.
Good luck~ :)

Yu Fan
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Post by Yu Fan »

I've viewed some topics says that it could be solved with binary sequence... but i can't imagine it.
someone helps me? :o

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Post by vedex »

I am not going to prove you why my solution is right. This is a very popular game called Nim. Lets say we have n stones a1, a2, ... , an
If, and only if, a1 xor a2 xor ... xor an = 0 =) 'NO'
a1 xor a2 xor ... xor an <> 0 =) 'YES'

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Post by Tanu »

Yah thats true i got accepted by this way
but can anyone let me know how it works.
Thanks in advance...
- Tanu :o

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