Part 1.
Find a 5-digit integer that consists of five consecutive digits, not necessarily in numerical order, such that, when multiplied by 8, the product is a 5-digit number consisting of the other five digits.

Part 2.
Find a 5-digit integer that consists of five consecutive digits, not necessarily in numerical order, such that, when divided by 8, the quotient is a 5-digit number consisting of the other five digits.

87456 / 8 = 10932

I think it is unique too (in not having leading 0). 

why? If it includes a 9 then the solution must work for both #1 and #2 which I believe Steve Herman about. (ok, I checked it myself but it is just eliminating possibilities :)

It must start with 8 or 9, so 8 and dividend must start with 1.
Then, next digit of dividend must be 0, so third digit of dividend must be 9 to get digit large enough and we are left with 2 possibilities, one of which worked.

Posted by Joel on 2006-10-07 19:09:52