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 Indexed Puzzle (Posted on 2004-07-19)
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.

1. The sum of the number's digits is a prime.
2. The product of the number's digits is odd.
3. Each of the number's digits is less than the next digit (if there is one).
4. No two of the number's digits are equal.
5. None of the number's digits is greater than 4.
6. The number has fewer than 6 digits.
7. The product of the number's digits is not divisible by 6.
8. The number is even.
9. No two of the number's digits differ by 1.
10. 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.

 See The Solution Submitted by SilverKnight Rating: 4.3750 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): Solution | Comment 14 of 22 |
(In reply to re: Solution by Bryan)

You are correct; I mistyped the statement number, and it should have read:

"As statement (2) is true, the number would be 2359, but that makes statement (0) true..."
 Posted by Federico Kereki on 2004-07-21 13:56:48

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