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

Home > Just Math
Point to 2012 (Posted on 2012-04-04) Difficulty: 3 of 5
Determine the minimum value of a positive integer N such that the four digits immediately following the decimal point in the base ten expansion of √N is 2012.

*** For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Explaining the arithmetic sequence. Comment 7 of 7 |
(In reply to re(2): computer solution by Charlie)

The difference of 5 can be explained.

(a+.20125^2) ≈ N

[(a+.20125)+5]^2 = (a+.20125)^2 +2*5*(a+.20125) + 5^2
= N + 10a + 27.0125

The key is the 27.0125 which is a near integer.

A much more persistent arithmetic sequence will be seen with a difference of 400 since my approximation .20125 = 161/800



  Posted by Jer on 2012-04-05 13:35:48

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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information