All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Squares Probability II (Posted on 2004-03-23) Difficulty: 3 of 5
You have created a 19 digit number with your 20 digit tiles as follows:

7_340_46_2010_51_49

Unfortunately someone knocked out 5 of the number tiles and placed them with the remaining number tile. The 6 tiles that are out are 6 3 2 8 9 3.

Without using any calculators, programs, or similar devices, what is the easiest way to figure out what the probability that my original 19-digit number will be a perfect square and what is this probability?

Note: The pesky "someone" also renumbered the number tiles so they were wrong and you couldn't tell what the right numbers are. This has been fixed to make the problem easier.

No Solution Yet Submitted by Gamer    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts with a computer (or a table of squares) | Comment 3 of 15 |
(In reply to without a calculator by Charlie)

It turns out that a number with 49 as its last two digits can be a perfect square only if the hundreds digit is even.  This has probability 1/2 of happening.  However, if it is even, the probability that is a square is 8 times what it otherwise would be, leaving us with just the same probability of four times the most naive estimate, i.e., it is still 1/1,250,000,000.
  Posted by Charlie on 2004-03-23 14:57:04

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information