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Topic: Take the last chip (Read 2936 times) |
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Sjoerd Job Postmus
Full Member
Posts: 228
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Re: Take the last chip
« Reply #25 on: May 25th, 2005, 11:01am » |
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Well, let's play the quickest solution possible, that's still efficient to play 
The pile contains 43546758343209876 chips.
If we take 43546758343209876/2 chips... The other can too, and we have lost. So we take (43546758343209876/2)-1 chips. That leaves us with (43546758343209876/2)+1 chips. Let's see what we make of that .
21773379171604939 left.
Now, because this is odd, we could resort to the eating-1 method, so that's not smart of the opponent, so he should eat one less, leaving 21773379171604940. Of course, we don't want to do the other a favor, so we eat this /2 -2 as well. Eating more isn't recommended, because it would result in a loss. Eating less? Sure! Maybe even just 2, but I wouldn't do that Would take too long to enumerate. So, that's a start!
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Deedlit
Senior Riddler
Posts: 476
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Re: Take the last chip
« Reply #26 on: May 25th, 2005, 11:08am » |
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on May 25th, 2005, 11:01am, Sjoerd Job Postmus wrote:Well, let's play the quickest solution possible, that's still efficient to play
The pile contains 43546758343209876 chips.
If we take 43546758343209876/2 chips... The other can too, and we have lost. So we take (43546758343209876/2)-1 chips. That leaves us with (43546758343209876/2)+1 chips. Let's see what we make of that .
21773379171604939 left.
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Fine, I'll take 3758980662122955 chips, leaving 18014398509481984 chips.
Your move. 
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Sjoerd Job Postmus
Full Member
Posts: 228
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Re: Take the last chip
« Reply #27 on: May 25th, 2005, 11:53am » |
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I could take one, and we have a winner?
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Deedlit
Senior Riddler
Posts: 476
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Re: Take the last chip
« Reply #28 on: May 25th, 2005, 11:57am » |
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Yes, I would be the winner. So you did not play optimally. (You can win from the starting position.)
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Sjoerd Job Postmus
Full Member
Posts: 228
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Re: Take the last chip
« Reply #29 on: May 25th, 2005, 12:00pm » |
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on May 25th, 2005, 11:57am, Deedlit wrote:| Yes, I would be the winner. So you did not play optimally. (You can win from the starting position.) |
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I see... so if I ate one at the start, I would've won? I don't think so...
Besides, I think I would win when I turn odd into even with one chip.
Just look at this, simplifying it to 5 chips left, after your move.
5 SJ 4
4 Dl 3
3 SJ 2
2 Dl 1
1 SJ 0 => SJ wins
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Deedlit
Senior Riddler
Posts: 476
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Re: Take the last chip
« Reply #30 on: May 25th, 2005, 12:04pm » |
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No, because the game starts with an even number of chips. In our game, I left you with an even number of chips, then you took one, so you lose.
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| « Last Edit: May 25th, 2005, 12:05pm by Deedlit » |
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Sjoerd Job Postmus
Full Member
Posts: 228
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Re: Take the last chip
« Reply #31 on: May 25th, 2005, 12:35pm » |
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on May 25th, 2005, 12:04pm, Deedlit wrote:| No, because the game starts with an even number of chips. In our game, I left you with an even number of chips, then you took one, so you lose. |
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Heh! I was basing your guess off my best one: 21773379171604940. It was in the middle of the text ... So you actually got the wrong guess.
So, I guess I should eat two instead, or any odd number.
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Deedlit
Senior Riddler
Posts: 476
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Re: Take the last chip
« Reply #32 on: May 25th, 2005, 2:35pm » |
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on May 25th, 2005, 12:35pm, Sjoerd Job Postmus wrote:
Heh! I was basing your guess off my best one: 21773379171604940. It was in the middle of the text ... So you actually got the wrong guess.
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Ah. Well, I could still leave 18014398509481984 chips - or, I could just take 4 chips.
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So, I guess I should eat two instead, or any odd number. |
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