There exists a number oddity with 3 different 4-digit numbers. One is 9801, where (98 + 01)^2 = 9801. It also works with 3025: (30+25)^2 = 3025.
What is the other number?
What is the smallest 6-digit number that would work?
(in other words, in a 6-digit number abcdef: abcdef=(abc+def)^2)

I made a grid on a spreadsheet with a vertical column from 1 to 99 and a horizontal row from 1 to 99.  In each of the 99*99 cells, I put the formula:   a^2+2ab+b^2-100a-b

finding the cells where the value = 0 gives the desired results

9801, 3025, 2025.

The actual formula I used to make the zeroes easier to spot was:
IF((a^2+2ab+b^2-100a-b)=0, "YES", "")   That way all the other cells were blank.

Should work for the 6 digit number too, just substitute 1000 in place of 100, and make a 999 by 999 grid.  Sure, my spreadsheet only has 282 columns; could do it in 4 sections.  But, as Rosanne Rosannadanna used to say:  "never mind"

And that's my story

 

Posted by Larry on 2004-04-03 14:11:17