Bernardo has forgotten the password of his safe. However he remembers that:

1. The number is a ten digit positive integer using each of the digits from 0 to 9 exactly once.
2. No digit is the same as the position which it occupies in the said number.
3. The sum of the 5th and 10th digits is a perfect square other than 9.
4. The sum of the 9th and 10th digits is a perfect cube.
5. The 2nd digit is an even number.
6. Zero is in the 3rd position.
7. The sum of the 4th, 6th and 8th digits is a single digit number.
8. The sum of the 2nd and 5th digits is a triangular number.
9. There is precisely one digit between 8 and 9.
10. 3 is next to 9 but not next to zero.

From the above clues, can you help Bernardo to crack the password to open the safe?

There's a quick way to deduce the answer if you make a (questionable) assumption. 

Clue 10 says that 3 is next to 9 but not next to 0.  The "but not next to 0" part could've been a total red herring, but let's assume it's necessary information to solve the puzzle. This implies that the 9 is two spots away from the 0, and that the 3 is next to 9 on the opposite side from the 0.  So we have either 0x93 or 39x0.

Clue 6 tells us that 0 is in the 3rd position, which rules out the case where the 3 and 9 are to the left of the 0.  So we have xx0x93xxxx.

From clue 9 we know the 7th digit must be 8: xx0x938xxx

From clue 3 we know the 10th digit must be 7:  xx0x938xx7

From clue 4 we know the 9th digit must be 1:  xx0x938x17

From clue 7 we know the 4th and 8th digits must be 2 and 4 in some order.  From clue 2 we know the 4th digit can't be 4, so we have: xx02938417

From clue 5 we know the 2nd digit must be 6, and then the 1st digit must be 5.

5602938417

 

 

Posted by tomarken on 2014-06-02 11:46:46