Multiply the first equation by 2, then add the equations.
We have .
Now, plug p in any equation and find q.
4) Plug x=4.2 and x=4.3 in equation and probably you'll obtain one negative value and one positive value.
5) Let x be the number of middle pieces.
The probability to pick one is .
On the other hand, the same probability is 1-0.008-0.164.
Equalize the two values and solve for x.