The Third Case of Mystery Number

There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. 

Given the following clues, what is the number?

1) Digit A is either a square number or a triangle number, but not both.

2) Digit B is either an even number or a cube number, but not both.

3) Digit C is either a cube number or a triangle number, but not both.

4) Digit D is either an odd number or a square number, but not both.

5) Digit E is either an odd number or a cube number, but not both.

6) Digit F is either an odd number or a triangle number, but not both.

7) Digit G is either an odd number or a prime number, but not both.

8) Digit H is either an even number or a square number, but not both.

9) Digit I is either a square number or a cube number, but not both.

10) Digit J is either a prime number or a triangle number, but not both.

11) A < B, C < D, E < F, G < H, I < J

12) A + B + C + D + E < F + G + H + I + J

Here is that MYSTERY number!


The FIRST Case of Mystery Number

The SECOND Case of Mystery Number