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

Home > Just Math
Wet Rain (Posted on 2013-05-19) Difficulty: 2 of 5

WIN*WIN=RETAIN


Just p&p.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Using a little brute force (spoiler) Comment 1 of 1
a) W must be three or higher, in order that the result is 6 digits

b) N must be 0, 1, 5, or 6 in order that N x N ends in N

c) Now we need IN X IN to end in IN.
   Obviously, N = 0 doesn't work, 
     because that would make IN = 00
   
   (10*I + N)^2  = (10*I + N) mod 100
   20*I*N + N^2  = (10*I + N) mod 100
   
   If N = 1, then 10*I = 0  mod 100 so I = 0
   If N = 5, then 25 = 10*I + 5 mod 100 so I = 2
   If N = 6, then 120*I + 36 = 10*I + 6 mod 100
                  10*I + 30 = 0 mod 100 so I = 7
                  
 d) So, the only possibilities are
    301  (too low)
    401
    601
    701
    801
    901
    325
    425
    625
    725
    825
    925
    376
    476
    576
    876
    976
    
  e) By brute force multiplication, only 425 * 425 = 180625 works 

  Posted by Steve Herman on 2013-05-19 12:51:18
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 (6)
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