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edited Jul 18, 2017 at 17:33

ZaMoC

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#Mathematica, 140141 bytes

B=Subsets;Count[Table[FreeQ[IntegerQCount[FreeQ[IntegerQ/@Sqrt[FromDigits/@s[[i]]]@#],1<0]1<0]&/@(FoldPairList[TakeDrop,{is,Length[s=Union@Select[B@Rest@B[r=#]#]&/@Flatten[Permutations/@IntegerPartitions[Length[s=#]],Sort@Flatten@#==Sort@r&]]}]1]),1>0]&

**input** (a list of digits) >[{1,6,4}]

#Mathematica, 140 bytes

B=Subsets;Count[Table[FreeQ[IntegerQ/@Sqrt[FromDigits/@s[[i]]],1<0],{i,Length[s=Union@Select[B@Rest@B[r=#],Sort@Flatten@#==Sort@r&]]}],1>0]&

**input** (a list of digits) >[{1,6,4}]

#Mathematica, 141 bytes

Count[FreeQ[IntegerQ/@Sqrt[FromDigits/@#],1<0]&/@(FoldPairList[TakeDrop,s,#]&/@Flatten[Permutations/@IntegerPartitions[Length[s=#]],1]),1>0]&

**input** (a list of digits) >[{1,6,4}]

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answered Jul 18, 2017 at 8:01

ZaMoC

25.5k
2
32
87

#Mathematica, 140 bytes

B=Subsets;Count[Table[FreeQ[IntegerQ/@Sqrt[FromDigits/@s[[i]]],1<0],{i,Length[s=Union@Select[B@Rest@B[r=#],Sort@Flatten@#==Sort@r&]]}],1>0]&

**input** (a list of digits) >[{1,6,4}]