Thread: Problem Solving

I have been working on this problem for about 2 hours now and can't figure out the answer. I have come up with multiple ideas but none are working.

The question is:
Two players play the following game: Thirteen markers are arranged in a circle. Each player removes either one marker or two contiguous markers (i.e markers that started out next to each other.) The player who takes the last marker wins. Is there a winning strategy for one of the players? If so, for which one, and what strategy? ( A winning is a rule for how to play your moves that will always lead to a win.)


Any help would be nice. Thank you in advance!

Originally Posted by matgrl

I have been working on this problem for about 2 hours now and can't figure out the answer. I have come up with multiple ideas but none are working.

The question is:
Two players play the following game: Thirteen markers are arranged in a circle. Each player removes either one marker or two contiguous markers (i.e markers that started out next to each other.) The player who takes the last marker wins. Is there a winning strategy for one of the players? If so, for which one, and what strategy? ( A winning is a rule for how to play your moves that will always lead to a win.)


Any help would be nice. Thank you in advance!

1. I'm not sure that I understand correctly the marked text (in blue)

2. In general: Make sure that there is a multiple of 3 left and your contrahent has to make her/his next move.

The marked text in blue is saying that a player can either take one marker or two markers that are next to each other at a time. They can choose either one to do. Does this make sense?

Originally Posted by matgrl

The marked text in blue is saying that a player can either take one marker or two markers that are next to each other at a time. They can choose either one to do. Does this make sense?

suppose the markers are arranged in the following order:

abcdefghijklma...

If a player removes e, will the other player be allowed to remove d and f in the next move ?

This looks like a variant of Nim.

No the player would only be able to be de, or dc since they are right next to each other.