# Save the damsel!

Logic Level 4

One fateful night, Brenda was walking home from her friend's birthday party when she suddenly got ambushed by her greedy aunt! Of course why Brenda's aunt is so greedy for money that she kidnapped her own niece is another story. Brenda was pale with shock but thankfully still had her faculties intact.

Locking Brenda up behind a gate, Brenda's aunt barked, "I have abducted you! The only way you can escape is to crack the 10-digit code of the padlock. To help you, here are some facts:

1. Every digit from 0 to 9 appears exactly once in the 10-digit code.

2. The leftmost number is the sum of the two numbers on its immediate right.

3. The leftmost number and the rightmost number differ by 1.

4. Interestingly enough, the second left number and the second right number differ by 2, to establish a pattern.

5. And more interesting still, just as the third left number and the third right number differ by 3, the fourth left number and the fourth right number differ by 4.

6. The number 0 occupies one of the middle two positions.

7. The sum of the left five numbers is a perfect square.

8. The sum of the right five numbers is a prime number.

9. The rightmost number is a perfect cube.

I believe I have given you enough information. Can you crack the code?

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