Sorry proof only is that a=1, b could still be 2..9 but
   913*923 933 943 953 963 973 983 993
842699 851829 860959 870089 879219 888349 897479 906609
the only palindrome is the last.

revised:

>We know (from our brutish numerical experiments) that the answer is 913*993. 
>Why does that HAVE to be?

>Well we know the answer must be of the form 9a3*9b3 because the first digit 
>must be maximal and so the last digit must also be a 9.

Now the carry to the first digit must be exactly 1 (not 0 or >1) Ie
 90000 <= (10000*9*(a+b))+(1000*a*b)+9
190000 >  (10000*9*(a+b))+(1000*a*b)+9

assume a<=b

let b be maximal (9)

 90000 <= (10000*9*(a+9))+(1000*a*9)+9

 10 000 <= (10000*(a+9))+(1000*a)+1

so a must be at least 1.

assume 2 for a and b minimal, ie 2. Then

190000 >  (10000*9*(2+2))+(1000*2*2)+9

190000 >  (360000)+(4000)+9

false, so a=1. Assume b=8


 90000 <= (10000*9*(9))+(1000*8)+9

 10000 <= 90000+(9%~1000*8)+1

 -79999 <= 8000%9

Not enough, so a=1 and b=9
ie 913*993

ie 913*993

greg
~krsnadas.org
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

Reply via email to