The usage of DuplicateFreeQ

Questions
1

See my following example:

In[347]:= x=Tuples[{0,1},3]
Select[x,! #[[1]]==#[[2]]==#[[3]]&]
Select[x,DuplicateFreeQ]

Out[347]= {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 
  0, 1}, {1, 1, 0}, {1, 1, 1}}

Out[348]= {{0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 
  1, 0}}

Out[349]= {}

I want to obtain the similar result as the second command by using the DuplicateFreeQ in the last command shown above. Why doesn’t my usage return any results?

Regards,
Zhao

2

Why doesn’t my usage return any results?

That is because all matrix rows contains duplicates.

SameQ could be used:

Select[x, ! SameQ @@ # &]
3

Nice. It does the trick:

In[12]:= xx=Tuples[{0,1},3]
Select[xx,! #[[1]]==#[[2]]==#[[3]]&]
%==Select[xx, ! SameQ @@ # &]==Select[xx, ! Equal @@ # &]

Out[12]= {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 
  0, 1}, {1, 1, 0}, {1, 1, 1}}

Out[13]= {{0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 
  1, 0}}

Out[14]= True

P.S. It seems that in this case, both SameQ and Equal work.