perplexus.info :: Probability : Neighbors or not?

Neighbors or not? (Posted on 2016-03-22)

If two cells are chosen randomly on a 8x8 chessboard what is the probability that they are neighbors (i.e. share a common side)?

No Solution Yet Submitted by Ady TZIDON

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

| Comment 2 of 3 |

There are 64C2 = 2016 ways to choose two random cells.

There are 8*7*2 = 112 ways to choose two adjacent cells (ways to place a 1x2 rectangle).

Then the probability is 112/2016 = 1/18.

Posted by Brian Smith on 2016-03-22 13:25:51

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info