Browse Teasers
Search Teasers

## Checkerboard Chances 2

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #42307 Fun: (2.14) Difficulty: (2.81) Category: Probability Submitted By: billy314

Timothy has a four by four checkerboard. He uses scissors to cut out each square from the board. He then randomly arranges the pieces into four rows and four columns. What is the probability that this layout is in a checkerboard pattern?

The first black piece can go in 16 different places since the checkerboard has an equal number of red and black squares (8 red and 8 black). The next piece however has only 7 different places it can go since one space is taken and it must be in a checkerboard pattern. The next piece has 6 different places it can go, and so on. Therefore, the number of ways the black pieces can be correctly put into the checkerboard is 16*7*6*5*4*3*2*1=16*7! (7! is 7*6*5*...*1). The first red piece has 8 different places it can be put. The next piece has seven. The next piece has six, and so on. The number of ways the red pieces can correctly be arranged is 8*7*6*5*4*3*2*1=8! (this is read 'eight factorial'). The total number of ways all the squares can be arranged (correctly or not) is 16! (16*15*14*...*1). The number of arrangements that form a checkerboard is 16*7!*8!. The probability that a checkerboard will be formed is 16*7!*8!/16!. Simplifying this fraction by canceling (a lot!) you get 1/6435 or about 0.01554%.
Hide

## What Next?

See another brain teaser just like this one...

Or, just get a random brain teaser

If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.

#### Users in Chat : cooltigerr1

Online Now: 5 users and 406 guests