Question: How do you solve a (large) system equations by applying 'rules'?

What I mean is, I have a set of variable, and a set of equations. The thing is, there are a lot of variables, and not enough equations to uniquely determine them unless the 'rules' are applied, which are:


1) all xi that exist are integers between 1 and 9, i.e. xi is in {1,2,3,4,5,6,7,8,9}

2) if xi exists, then xi<>xi+1 AND xi<>xi+10


The reason I keep saying "if xi exists" or whatever is because not i does not run from 1 to n or anything like that.

If it helps, here is the set of variables:
vars := {x[22], x[23], x[26], x[27], x[28], x[32], x[33], x[35], x[36], x[37], x[38], x[42], x[43], x[44], x[45], x[46], x[53], x[54], x[56], x[57], x[64], x[65], x[66], x[67], x[68], x[72], x[73], x[74], x[75], x[77], x[78], x[82], x[83], x[84], x[87], x[88]};
 

and the set of equations:
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]};

 

Does anyone have any ideas as to how I could teach Maple these 'rules'? Preferably before it tries to find ALL of the solutions, because otherwise it may take a very long time first finding them all and then searching through them to find the one that satisfies the rules above.

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