I spent longer than I needed to on this. Here is the answer I got and the process I went through.

**Quote:**

• 0+0+0+0 = 4, so-------------------------------------------->0 = 1

• 5+5+5+5 = 0, so-------------------------------------------->5 = 0

• 1+1+1+1 = 0, so-------------------------------------------->1 = 0

• 9+9+9+9 = 4, so-------------------------------------------->9 = 1

• 8+0+8+8 = 7,

and 0 = 1, so 8+8+8 = 7-1 = 6------------------------------>8 = 2

• 2+0+4+8 = 4,

and 0 = 1 and 8 = 2, so 2+4 = 4-2-1 = 1------------------->one of 2 or 4 = 0, and the other = 1

• 1+2+3+4 = 1,

and 1 = 0 and (2+4) = 1, so 3 = 1-1 = 0------------------->3 = 0

• 3+0+8+4 = 4,

and 3 = 0 and 0 = 1 and 8 = 2, so 4 = 4-2-1 = 1---------->4 = 1

• Since 4 = 1, 2 ≠ 1 2 = 0

• 6+3+1+1 = 1,

and 3 = 0 and 1 = 0, so 6 = 1------------------------------->6 = 1

• SO,----------------------------------------------------------->8456 = 2+1+0+1 = 4

The statements 5749=2, and 7685=3 are not needed to solve the riddle if you do it this way

I realized at the end that it was much simpler than I made it. :)