Comments on: Conundrum: Nim, Part I http://www.shakespeareteacher.com/blog/archives/462 Fri, 05 Dec 2008 02:31:43 +0000 http://wordpress.org/?v=2.6.1 By: Bill http://www.shakespeareteacher.com/blog/archives/462#comment-78329 Bill Wed, 18 Jun 2008 00:33:23 +0000 http://www.shakespeareteacher.com/blog/archives/462#comment-78329 This was solved elsewhere, but I'll post the answer here. You can force a win by taking one coin from any odd numbered pile. I would take a coin from Pile 5, leaving 1-2-3-4-4. The first three piles of 1-2-3 you can deal with as described above. As for the other two piles of 4, whatever he takes from one, you can take from the other. This was solved elsewhere, but I’ll post the answer here.

You can force a win by taking one coin from any odd numbered pile.

I would take a coin from Pile 5, leaving 1-2-3-4-4.

The first three piles of 1-2-3 you can deal with as described above. As for the other two piles of 4, whatever he takes from one, you can take from the other.

]]> By: Bill http://www.shakespeareteacher.com/blog/archives/462#comment-48782 Bill Thu, 22 May 2008 09:25:57 +0000 http://www.shakespeareteacher.com/blog/archives/462#comment-48782 This strategy will not guarantee victory. Let's say you clear out Pile 5. Then Iachimo clears out Pile 4. (Or you clear out Pile 4, and Iachimo clears out Pile 5.) Now you're left with: 1. O 2. OO 3. OOO 4. 5. And you're in trouble. If you take one coin from Pile 3, Iachimo takes the coin from Pile 1 (or vice versa) leaving you with two piles of two. Whatever you take from one pile, he will take from the other. If you take two coins from Pile 3, Iachimo takes both coins from Pile 2 (or vice versa), leaving you with two piles of one. You take one coin, and he takes the other. If you take all three coins from Pile 3, he takes one coin from Pile 2 (or vice versa), leaving you with two piles of one as above. There are actually three distinct moves you can make if you go first that will guarantee a win, even if you are playing someone as crafty as Iachimo. Can you find one of them? This strategy will not guarantee victory. Let’s say you clear out Pile 5. Then Iachimo clears out Pile 4. (Or you clear out Pile 4, and Iachimo clears out Pile 5.)

Now you’re left with:

1. O
2. OO
3. OOO
4.
5.

And you’re in trouble.

If you take one coin from Pile 3, Iachimo takes the coin from Pile 1 (or vice versa) leaving you with two piles of two. Whatever you take from one pile, he will take from the other.

If you take two coins from Pile 3, Iachimo takes both coins from Pile 2 (or vice versa), leaving you with two piles of one. You take one coin, and he takes the other.

If you take all three coins from Pile 3, he takes one coin from Pile 2 (or vice versa), leaving you with two piles of one as above.

There are actually three distinct moves you can make if you go first that will guarantee a win, even if you are playing someone as crafty as Iachimo. Can you find one of them?

]]> By: Neel Mehta http://www.shakespeareteacher.com/blog/archives/462#comment-48682 Neel Mehta Thu, 22 May 2008 06:36:10 +0000 http://www.shakespeareteacher.com/blog/archives/462#comment-48682 Addendum: Say Iachimo decides to extend the game as long as possible in the hopes that you slip up. Well, don't slip up. Your first move, of course, is to empty out a pile (any will suffice) so that 4 piles remain. Then, as each of you remove 1-2 coins at a time, make sure that Iachimo can't leave behind either 2 or 4 piles with only one coin each. If that happens, then he'll win. Addendum: Say Iachimo decides to extend the game as long as possible in the hopes that you slip up. Well, don’t slip up. Your first move, of course, is to empty out a pile (any will suffice) so that 4 piles remain. Then, as each of you remove 1-2 coins at a time, make sure that Iachimo can’t leave behind either 2 or 4 piles with only one coin each. If that happens, then he’ll win.

]]> By: Neel Mehta http://www.shakespeareteacher.com/blog/archives/462#comment-48680 Neel Mehta Thu, 22 May 2008 06:29:02 +0000 http://www.shakespeareteacher.com/blog/archives/462#comment-48680 Like Tic-Tac-Toe (and maybe Global Thermonuclear War), the odds seem to be heavily in your favor if you play first. I don't think you have to go to a specific pile for your first move, but your goal in general is to keep an even number of piles. (This way you can guarantee that it will be your turn when only one pile remains.) Iachimo can extend the game as long as he wants, but he's not going to win. I'm not sure of a good way to demonstrate this because there are so many ways the game can go. But I will suggest the following format for anyone else who wants to depict each move: O OO OOO OOOO OOOOO Like Tic-Tac-Toe (and maybe Global Thermonuclear War), the odds seem to be heavily in your favor if you play first. I don’t think you have to go to a specific pile for your first move, but your goal in general is to keep an even number of piles. (This way you can guarantee that it will be your turn when only one pile remains.) Iachimo can extend the game as long as he wants, but he’s not going to win.

I’m not sure of a good way to demonstrate this because there are so many ways the game can go. But I will suggest the following format for anyone else who wants to depict each move:

O
OO
OOO
OOOO
OOOOO

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