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.

12345 and 98760 work.

I haven't looked for other solutions, but clearly the first number must start with the digits 12, otherwise the product is over 100000.

And then the third digit must be 3, to avoid duplicate digits in the product.

And then the fourth digit must be 4, to avoid duplicate digits in the product.

And then the fifth digit must be five.

So I guess that this solution is unique.

Posted by Steve Herman on 2006-10-07 08:22:22