Alfonso 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.
- The sum of the 2nd, 5th, 6th and 8th digits is a single digit number.
- The 4th digit is a perfect square.
- The 3rd digit is 1
- The sum of the 4th and 7th digits is a perfect square.
- The value of the 10th digit is twice that of the 2nd digit.
- The product of the 4th digit and the 6th digit is equal to that of the 2nd digit and the 10th digit.
- 5 is next to 6 but not 4.
From the above clues, can you help Alfonso to crack the password to open the safe?
a) From Clue 4, the third digit is 1
b) Then, from clue 2, the 2nd, 5th, 6th and 8th digits must be 0, 2, 3, and 4, in some order
c) Then, from clue 3, the 4th digit must be 9
d) Then, from clue 5, the 7th digit must be 7
e) From clue 6, the 2nd and 10th digit must be either 3 and 6 or 4 and 8
f) From clue 7, the 2nd and 10th digits must be 3 and 6, not 4 and 8. And the 6th digit must be a 2.
So far, we have *319*27**6
g) From clue 8, the 9th digit must be 5. And the 8th digit therefore cannot be 4, so it must be 0. Then the 5th digit must be 4, so the remaining number (8) goes in the remaining spot (the 1st)
Final answer: 8319427056
Analytical Solution (spoiler)
