atherine and Heathcliff were Sunday driving
in the country. They were looking for a secluded lake they had been told about.
As their vehicle crested a short hill, they came to a fork in the road.
Catherine stopped the car. “Do you remember,” she asked Heathcliff, “If we were
told to go left or right at this fork?”
Heathcliff couldn’t remember the directions.
As he thought back, his mind wandered, and he came up with another logic
“Cath”, he began. “Imagine there were a
couple of guides here and they could give us directions. Now, suppose one of them always told the
truth, but the other one will always told a lie. You can assume that each guide
knows whether the other is a liar or a truth teller.”“Finally”, he continued.
“Let’s also assume that both guides know which road leads to the lake.
“The puzzle Cath”, he finished, “is to ask
a single question of one of the guides and then determine which road to take.
Catherine knew Heathcliff could always
distract her like this. She wanted to continue driving, and she was considering
flipping a coin to decide which road to take. But, she was a little intrigued
by Heathcliff’s puzzle.
couldn’t just point down a road and ask the first guide “Is this the road to
the lake?” There was only a fifty-fifty chance the guide she chose would be the
truth teller. So, that approach would be wrong as often as it was right. She
wondered if there was a question that each guide would answer the same way.
How, she wondered, would they answer the question “Are you a liar?” upon
reflection, Catherine realized that both guides would say “No”. She also
realized that both guides would say “Yes”, if she asked “Is the other guide a
Catherine felt that she was onto something,
but she wasn’t sure how to proceed. She wondered, “What if I ask them something
that I know is true?” “Does 2 plus 2 equal 4?” “That would identify the truth
teller,” she reasoned, “But, I only have one question. What if I asked, “Would
the other guide tell me that 2 plus 2 equals 4”? Both guides would answer “No”. Then, in a flash of inspiration, Catherine
had solved the puzzle.
“Ok Heath”, I’ve got it, Catherine said.
“I’d ask one guide if the other guide would tell me that the left fork led to
the lake.” If the answer was “Yes”, I’d take the right fork and if the answer
was “No”, then I’d take the left road.”
“Now” she asked, “Tell me the truth. Which
way should we go?”