Question: system of equation

Boy, this program sure makes me feel like an idiot.  (I am a full professor at a top university, but maple has turned me into an idiot.)

so, here's my stupid question now:

(for those of you who do statistics, this is the principal stratification problem in causal inference.  Eventually, I'll replace equations 9-11 with other conditions.

I hope to show my class this.)

eq := p0+p1+p2+p3+p4+p5 = Pi11,
p8+p9 = sigma11,
p6+p7 = Pi10,
p10+p11 = sigma10,
p0+p1 = Pi01,
p3+p8 = sigma01,
p2+p6 = Pi00,
p4+p5+p7+p9+p10+p11 = sigma00,
p3 = 0,
p5 = 0,
p7 = 0,
p0+p1+p2+p3+p4+p5+p6+p7+p8+p9+p10+p11 = 1;

sol1 := solve({eq}, {p0, p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11});

Why won't this solve?  Maple doesn't do anything--it just sits there.

When I look at specific elements of the equation vector, they look ok to me (eq[12]).  Unless I'm not counting properly, the second vector I feed to solve has 12 elements. 

I also can get it to work for simpler problems (y-x=2; x+3=y)

I realize this is a lot of equations but it's 12 equations and 12 unknowns.  And I know the solutoin.  (I just want maple to generate it.)    I want the p's solved in terms of the pi's and sigma's.

What stupid mistake am I making now?

In an ideal world, I'd actually be storing sigma in a 2x2 matrix.  Same thing with pi's.  But I can live without that--

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