A four digit number is squared to form an eight digit number. The center four digits of that square form the four digit number. Find all possible four digit numbers.

(If 'abcd' was the four digit number, then the eight digit number would look like 'wxabcdyz'.)

I'm surprised no one else bothered mentioning them but there are two further solutions with leading zeroes allowed (not technically 4 or 8 digit numbers but what the heck)

0100² = 00 0100 00

2500² = 06 2500 00

It should not be surprising there are so few.  There are only 10000 numbers to check and each has a 1/10000 chance of working if the digits were random.  This means we should expect only one solution.  The fact there are 4 without some kind of obvious pattern could be seen as kind of suprising.

-Jer

Posted by Jer on 2004-11-29 17:08:37