#### packman

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• Posts: 226
##### 六分巧克力, and answer is here
« on: 七月 20, 2004, 09:25:41 am »
OK, here's another M&M problem.  It's more like a betting game at the corner of the street while the dealer lures the people to play and lose money, if they don't know how to win.  If you know the trick, you can become a dealer too, and win some money during the coffee break at work...  I will post the answer this Friday.

#### 万精油

• Hero Member
• Posts: 1831
##### 六分巧克力, and answer is here
« Reply #1 on: 七月 20, 2004, 10:59:38 am »
This is the classic of all Nim like problem. In fact, I think this is the earliest version. All the other variations are derived from this version.

For this particular problem, (3,5,7) is just interesting enough to put on a coffee table, and easy enough to do it in mind. If there are more M&M's on the table, figuring out all the b***** pattern in head can be quite hard, I tried it for bigger number once (with my son), and got mixed up two steps into the game.

Anyway, this is a good puzzle, I hope other people like it.

I used ***** in the above paragraph so that it will not spoil other people's fun of solving this puzzle.

#### 差不多

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• Posts: 10
##### 六分巧克力, and answer is here
« Reply #2 on: 七月 20, 2004, 12:22:36 pm »

#### packman

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• Posts: 226
##### 六分巧克力, and answer is here
« Reply #3 on: 七月 20, 2004, 12:33:19 pm »
123, 111 and xxo are the final winning combinations. But how do you get there?
What I am asking are the intermediate winning combinations, all of them.

#### packman

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• Posts: 226
##### 六分巧克力, and answer is here
« Reply #4 on: 七月 23, 2004, 09:14:53 am »
The winning combinations are:(doesn't matter what color)
0xx
111
123
145
246
357
........

You can add more numbers to the previous winning combo to make a new one, but it is harder and harder, as Prof.10K pointed out earlier.

#### 万精油

• Hero Member
• Posts: 1831
##### 六分巧克力, and answer is here
« Reply #5 on: 七月 23, 2004, 09:46:38 am »
From your answer I can see that you do not know the general answer to this question. Given starting point (a,b,c), what is the general winning strategy. e.g. if the start condition is (100,200,300), what do you do? When I said it is hard, I meant it is hard to do it in head, but it is not hard to do it on a piece of paper or by a computer program.

BTW, 357 is not a winning combination (if 111 is).

#### packman

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• Posts: 226
##### 六分巧克力, and answer is here
« Reply #6 on: 七月 23, 2004, 10:22:46 am »
Sorry, I posted wrong. Should be like this:

To ensure winning, you have to leave your opponent to one of these combinations:
0xx
111
123
145
246

I never thought of more than that. Prof.10k, please give us a lecture.

#### packman

• Full Member
• Posts: 226
##### 六分巧克力, and answer is here
« Reply #7 on: 七月 23, 2004, 10:23:21 am »
Sorry, I posted wrong. Should be like this:

To ensure winning, you have to leave your opponent to one of these combinations:
0xx
111
123
145
246

I never thought of more than that. Prof.10k, please give us a lecture.

#### froid

• Newbie
• Posts: 16
##### 六分巧克力, and answer is here
« Reply #8 on: 七月 23, 2004, 10:49:21 am »

http://web.usna.navy.mil/~wdj/book/node10.html