Puzzle #185: Marker on a 9×9 Board

This is a wonderful puzzle, this time from a relatively lesser used source – A Moscow Math Circle, Week by week Problem Sets, by Sergey Dorichenko.

One marker is placed in the center of a 9×9 board. Anisha and Arushi take turns moving the marker to one of the adjacent squares – one sharing a side – provided that this square has never been occupied by the marker. Anisha goes first. The first player unable to move loses. Which of the players can guarantee a win?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy father’s day!

This entry was posted in Puzzles and tagged , . Bookmark the permalink.

2 Responses to Puzzle #185: Marker on a 9×9 Board

  1. Prakhar says:

    The first person is likely to lose. If one cell containing the initial coin is removed, we have even number of cells left. If second person were trapped, first one has made odd or even moves and the second one has made the opposite. Either ways , o + e = o which is not equal to even cells. If first person was trapped, the number of moves is odd + odd or even + even, thereby an even number of cells used up. Therefore only the second move makes you ensure victory

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s