The Mysterious Code
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---
The sum of the middle two digits is a Square Number.
The sum of the middle four digits is a Cube number
The net difference between the first and tenth digit is \(2\)
The net difference between the second and ninth digit is \(3\)
The net difference between the third and eighth digit is \(4\)
The sum of the first five digits is a Prime number
The sum of the last five digits is a Triangular number
The sum of the digits in odd positions (first, third, fifth, seventh and ninth digits) is an Odd number
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?"