wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> abcbaaaba and perfect square puzzle
        
(Message started by: K Sengupta on Apr 23^rd, 2009, 6:25am)

Title: abcbaaaba and perfect square puzzle
Post by K Sengupta on Apr 23^rd, 2009, 6:25am

Determine the minimum value of a perfect square having the form abcbaaaba, where each of a, b and c represents a different decimal digit from 0 to 9, and a is nonzero.

Title: Re: abcbaaaba and perfect square puzzle
Post by Grimbal on Apr 23^rd, 2009, 7:51am

a=1
c=8
b=+
;D

Title: Re: abcbaaaba and perfect square puzzle
Post by towr on Apr 23^rd, 2009, 8:31am

on 04/23/09 at 07:51:23, Grimbal wrote:

a=1
c=8
b=+
;D

Now if only + was a decimal digit ;)

Title: Re: abcbaaaba and perfect square puzzle
Post by Peterman on Apr 23^rd, 2009, 10:28am

There is only one:
[hideb]a=1,b=6,c=5[/hideb]

Title: Re: abcbaaaba and perfect square puzzle
Post by towr on Apr 23^rd, 2009, 11:15am

Did you just do a computer search? Or did you have a more clever way to find it?

Title: Re: abcbaaaba and perfect square puzzle
Post by Peterman on May 6^th, 2009, 7:11am

There are only nine possible endings of the form ..xxYx, viz 1121, 1161, 4404, 4464, 4484, 6656, 6676, 9929, 9969. But it was in fact much quicker to just do the search; there are only just over 21,000 possible values of the square root and a program only takes a minute or so to write.