Here is a numbered list of statements, some true, some false, which refer to a specific number (unique positive integer, base 10).

It just so happens that if a statement is true then its index number appears among the number's digits, and if a statement is false then its index number does not appear among the number's digits.

0. The sum of the number's digits is a prime.
1. The product of the number's digits is odd.
2. Each of the number's digits is less than the next digit (if there is one).
3. No two of the number's digits are equal.
4. None of the number's digits is greater than 4.
5. The number has fewer than 6 digits.
6. The product of the number's digits is not divisible by 6.
7. The number is even.
8. No two of the number's digits differ by 1.
9. At least one of the number's digits is equal to the sum of two other digits. (Any of the digits may be equal, as long as all 3 digits are distinct... for example: {2, 2, 4} or {2, 3, 5} )

Find the number.

If 0 is divisible by all numbers then there are at least several answers:
80555
85055
85505
8005

If zero is not divisible by all numbers (including six) then there is only one (as I suppose - but didn't have time to check really good) correct answer:

97532

Best wishes,
Rafal

Posted by Rafal on 2004-09-10 08:55:01