In “Him Diddle
Riddle,” the girls run themselves ragged trying to solve a
series of puzzles and challenges put to them by
“Him.” One requires them to choose between Ms. Keane
and an exact duplicate of her; this sequence has sparked much
debate among fans. It therefore deserves some scrutiny.
The Setup
Two women, each looking and sounding exactly like
Ms. Keane, are suspended over a shark tank. One is the genuine
article, while the other is a phony. “Him” tells the
girls that the real Keane will answer any question truthfully,
but the phony will answer with a lie. The girls are allowed to
ask them one question before choosing the one they think is real.
If they pick correctly, her life will be spared; otherwise, both
will be fed to the sharks.
The Approach
The girls consider and
discard a few useless questions before Blossom comes up with
this:
"Ms. Keanes...who will the other Ms. Keane say is the real
Ms. Keane?"
From Keane 2, she gets this answer: "She would say that I was
the real Ms. Keane!"
Keane 1 responds by saying, "And she would say that she was
the real Ms. Keane!"
Blossom reasons it out and
decides that Keane 2 is the real one, and "Him" concedes defeat.
The problem is that she gets it dead wrong.
The Logic
Suppose that Keane 2 (K2)
is real and Keane 1 (K1) is the phony. Each one knows who is who.
K2 knows that K1 will lie and call herself the real one. Since K2
tells the truth, she will say as much to Blossom. K1 knows that
K2 will tell the truth and name herself as real. However, K1 will
answer with a lie, saying that K2 will call her the real one. The
result is that both Keanes will point the finger at K1, so it is
only necessary to ask one of them. Note that these answers are
the opposite of the ones given.
If K1 is real instead, the
same logic applies with K1 and K2 reversed and Blossom gets the
answers in the previous section. She correctly reasons out the
situation, but reaches the wrong conclusion. Both answers reveal
which one is the phony, so the correct solution is to take the
other choice. According to the rules of the game, choosing K2
should have led to both Keanes becoming shark bait.
In “Him Diddle
Riddle,” the girls run themselves ragged trying to solve a
series of puzzles and challenges put to them by
“Him.” One requires them to choose between Ms. Keane
and an exact duplicate of her; this sequence has sparked much
debate among fans. It therefore deserves some scrutiny.
Two women, each looking and sounding exactly like
Ms. Keane, are suspended over a shark tank. One is the genuine
article, while the other is a phony. “Him” tells the
girls that the real Keane will answer any question truthfully,
but the phony will answer with a lie. The girls are allowed to
ask them one question before choosing the one they think is real.
If they pick correctly, her life will be spared; otherwise, both
will be fed to the sharks.
The girls consider and
discard a few useless questions before Blossom comes up with
this:
Blossom reasons it out and
decides that Keane 2 is the real one, and "Him" concedes defeat.
The problem is that she gets it dead wrong.
Suppose that Keane 2 (K2)
is real and Keane 1 (K1) is the phony. Each one knows who is who.
K2 knows that K1 will lie and call herself the real one. Since K2
tells the truth, she will say as much to Blossom. K1 knows that
K2 will tell the truth and name herself as real. However, K1 will
answer with a lie, saying that K2 will call her the real one. The
result is that both Keanes will point the finger at K1, so it is
only necessary to ask one of them. Note that these answers are
the opposite of the ones given.
If K1 is real instead, the
same logic applies with K1 and K2 reversed and Blossom gets the
answers in the previous section. She correctly reasons out the
situation, but reaches the wrong conclusion. Both answers reveal
which one is the phony, so the correct solution is to take the
other choice. According to the rules of the game, choosing K2
should have led to both Keanes becoming shark bait.