Bernardo has forgotten the password of his safe. However he remembers that:
- The number is a ten digit positive integer using each of the digits from 0 to 9 exactly once.
- No digit is the same as the position which it occupies in the said number.
- The sum of the 5th and 10th digits is a perfect square other than 9.
- The sum of the 9th and 10th digits is a perfect cube.
- The 2nd digit is an even number.
- Zero is in the 3rd position.
- The sum of the 4th, 6th and 8th digits is a single digit number.
- The sum of the 2nd and 5th digits is a triangular number.
- There is precisely one digit between 8 and 9.
- 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.
Posted by tomarken
on 2014-06-02 11:46:46