Brain Teasers Optical Illusions Puzzle Hunts Codes & Ciphers Mechanical Puzzles
Personal Links
Browse Teasers
Search Teasers

Secret Santas II

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

 

Puzzle ID:#43900
Fun:*** (2.66)
Difficulty:*** (2.56)
Category:Probability
Submitted By:javaguru*us**

 

 

 



A group of ten friends decide to exchange gifts as secret Santas. Each person writes his or her name on a piece of paper and puts it in a hat. Then each person randomly draws a name from the hat to determine who has him as his or her secret Santa. The secret Santa then makes a gift for the person whose name he drew.

When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.

What is the probability that the 10 friends holding hands form a single continuous circle?



Answer

1/10

For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is

(n-1)! / n!

Since n! = (n-1)! * n (for n > 1), this can be rewritten as

(n-1)! / (n*(n-1)!)

Factoring out the (n-1)! from the numerator and denominator leaves

1/n

as the probability.

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.

 





Back to Top
   


Online Now
9 users and 600 guests

Users In Chat
Aviator
Follow Braingle!
Tap into all 20,000+ of our brain teasers, riddles and puzzles on your iPhone or iPad.

Braingle in the iTunes App Store
Copyright © 1999-2017 | FAQ | Widgets | Links | Green | Subscribe | Contact | Privacy | Conditions | Advertise | Braingle Time: 5:51 pm
Sign In Create a free account