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

Home > Just Math
Perfect Square Digit (Posted on 2015-08-17) Difficulty: 3 of 5
The last two digits of a perfect square N, having at least 3 digits, is 09 (in this order).

Is the hundreds digit of N always even? Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution Comment 2 of 2 |
x²= N
For N to end in 9, x must end in 3 or 7.

For N to end in 09, x must be of the form 50n±3
(50n±3)²=2500n²±300n+9
Notice the hundreds place digits are both odd.  Since n² and n also have the same parity, the sum will always be even.

If you check
(50n±13)² ends in 69
(50n±23)² ends in 29
(50n±33)² ends in 89
(50n±43)² ends in 49



  Posted by Jer on 2015-08-18 08:51:44
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 (5)
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