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Topic: An indexed number (Read 201 times) |
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pcbouhid
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An indexed number
« on: Nov 27th, 2005, 5:56am » |
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Below there is a numbered list of statements, some true, some false, which refer to a specific number (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. Find the number.
A "triple" means any sub-string of 3 consecutive digits, (consecutive by position, not value).
(0) The number does not have 2 equal adjacent digits.
(1) At least one digit is an odd prime.
(2) The number is odd.
(3) The third digit of any triple is equal to the first digit plus the second digit (mod 10).
(4) The last 3 digits are primes.
(5) The third digit of any triple is equal to the first digit minus the second digit (mod 10).
(6) Exactly one digit value is prime.
(7) The third digit of any triple is equal to the second digit minus the first digit (mod 10).
(8) The last 2 digits are both squares.
(9) The last 2 digits are both even.
The solution is unique.
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