Question: How do I apply rules to a large system of linear equations?

I have this system:
 

alleqs := {23 = x[22]+x[32]+x[42], 30 = x[23]+x[33]+x[43]+x[53], 27 = x[26]+x[36]+x[46]+x[56]+x[66], 12 = x[27]+x[37], 16 = x[28]+x[38], 17 = x[35]+x[45], 15 = x[44]+x[54]+x[64]+x[74]+x[84], 12 = x[57]+x[67]+x[77]+x[87], 7 = x[65]+x[75], 7 = x[68]+x[78]+x[88], 11 = x[72]+x[82], 10 = x[73]+x[83], 5 = x[77]+x[78], 3 = x[87]+x[88], 16 = x[22]+x[23], 17 = x[32]+x[33], 35 = x[42]+x[43]+x[44]+x[45]+x[46], 21 = x[72]+x[73]+x[74]+x[75], 6 = x[82]+x[83]+x[84], 7 = x[53]+x[54], 16 = x[64]+x[65]+x[66]+x[67]+x[68], 29 = x[35]+x[36]+x[37]+x[38], 24 = x[26]+x[27]+x[28], 8 = x[56]+x[57]};
 

which I want to solve for the variables in it, but by using the rules that all x[i] must be integers between 1 and 9 inclusive, and if x[i] and x[j] are in an equation together, they are not equal.
Does anyone have any idea how I could go about this? I have run out of ideas as to how to convey these rules to Maple code. Please help!

Thanks