# The Mysterious Code

Logic Level 4

You wake up in a locked cell, a bit shaken up but with all faculties intact. When you get to the cell-door you see a Number Pad with an attached note that has the following instructions...

"I am Professor Mad Math. I have imprisoned you! The only way to escape is to punch in the correct Code into the Number Pad. The $10$ digit Code is made up of digits $0-9$ inclusive, each digit used exactly once. These are the clues to crack my Code---

1. The sum of the middle two digits is a Square Number.

2. The sum of the middle four digits is a Cube number

3. The net difference between the first and tenth digit is $2$

4. The net difference between the second and ninth digit is $3$

5. The net difference between the third and eighth digit is $4$

6. The sum of the first five digits is a Prime number

7. The sum of the last five digits is a Triangular number

8. The sum of the digits in odd positions (first, third, fifth, seventh and ninth digits) is an Odd number

9. The digit $4$ is somewhere in the first five positions

I believe I have given you more than adequate information. Can you crack the Code?"

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