Where is the mistake in this proof by induction that all women have the same hair color?

induction/same.hair.color New

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Problem

Where is the mistake in this proof by induction that all women have the
same hair color?

Let me define an equi-colored set of women: just a set of women who have
the same hair color.  All sets of 1 woman are equi-colored: obvious!
I'm now going to use the standard proof by induction: if I assume that
all sets of "n" women are equi-colored and then I can prove that any set
of "n+1" women is equi-colored, I made the job.  Let's draw this set

   X  X  X  X  X  X  X  X  X  X  X  X  X  X  X   <- n+1 women
   ----------------------------------------      this set is of n women
      ----------------------------------------   idem

As I assume that the 2 sets of n women are equi-colored, you can see that
the whole sample is also equi-colored.  No?

-- Alain <buysxx@axcrnb.cern.ch>

[ Editor: the posting was titled "All the women are blonde". ]

Show solution

This sounds stupid but as a matter of fact, this is a classic one.  Your
proof does not stand when n=1.

-- Wentao Chen <wenchen@cs.yale.edu>