is there a better way to do constraint logic programming in Mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg80786] is there a better way to do constraint logic programming in Mathematica?*From*: "sdw" <warwick at jps.net>*Date*: Sat, 1 Sep 2007 00:36:23 -0400 (EDT)*Organization*: Posted via Supernews, http://www.supernews.com

simplified constraint programming example in Mathematica: find a set of numbers that add to a particular value - numbers cannot be the same note huge timing problem as we go up in variables Above 5, it hung... I was really hoping Mathematica had a decent constraint solver, but not sure now!! ---- sumgroup[num_] := (vars = Flatten @ Table[ ToExpression["x" <> ToString[i]], {i, 1, num}] ; r1 = And @@ Map[( 0 < # < 10) & , vars]; Print [r1]; r2 = ( Plus @@ vars) == Round[ 9 num /2]; Print [r2]; r3 = And @@ Rest @Union @ Flatten @ Table[vars[[i]] != vars[[j]], {i, 1, num}, {j, i, num}] ; Print[r3]; tim = Timing[FindInstance[r1 && r2 && r3, vars, Integers]]; Print[tim] ; Print[]); For[ nn = 2, nn < 6, nn++, sumgroup[nn]] 0 < x1 < 10 && 0 < x2 < 10 x1 + x2 == 9 x1 != x2 {5.42101*10^-19, {{x1 -> 1, x2 -> 8}}} "" 0 < x1 < 10 && 0 < x2 < 10 && 0 < x3 < 10 x1 + x2 + x3 == 14 x1 != x2 && x1 != x3 && x2 != x3 {5.42101*10^-19, {{x1 -> 1, x2 -> 4, x3 -> 9}}} "" 0 < x1 < 10 && 0 < x2 < 10 && 0 < x3 < 10 && 0 < x4 < 10 x1 + x2 + x3 + x4 == 18 x1 != x2 && x1 != x3 && x1 != x4 && x2 != x3 && x2 != x4 && x3 = != x4 {0.094, {{x1 -> 2, x2 -> 3, x3 -> 4, x4 -> 9}}} "" 0 < x1 < 10 && 0 < x2 < 10 && 0 < x3 < 10 && 0 < x4 < 10 && 0 < x5 < 10 x1 + x2 + x3 + x4 + x5 == 22 x1 != x2 && x1 != x3 && x1 != x4 && x1 != x5 && x2 != x3 && x2 = != x4 && x2 != x5 && x3 != x4 && x3 != x5 && x4 != x5 {33.062, {{x1 -> 1, x2 -> 2, x3 -> 3, x4 -> 7, x5 -> 9}}} ""

**Follow-Ups**:**Re: is there a better way to do constraint logic***From:*danl@wolfram.com