Yet Another Liar Truth-teller Problem

Logic Level 1

There are two tribes on an island. Natives from the Truth-teller Tribe will always speak the truth, while natives from the Liar Tribe will always lie.

Derek comes to a fork in the road. He wants to find the correct road to the Truth-teller Tribe. Two natives, where at least one of them is a truth-teller, made the following statements.

A : The left road leads to the Truth-teller Tribe.

B : If I were him, I would say that the right road leads to the Truth-teller Tribe.

A : Well, if I were him, I would say that the right road leads to the Truth-teller Tribe.

Which way should Derek follow?

The right road Can't be determined Neither The left road

Wind Quotidian by Wind Quotidian , 20, Malaysia

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2 solutions

Jonathan Quarrie
Jan 6, 2018

With both A and B stating that the other native would say that the right road leads to the Truth-teller Tribe, this forms 2 different generalisations.

  1. They are both from the Truth-teller Tribe, and the right road is the correct road.
  2. One of them is from the Liar Tribe, and the left road is actually the correct road (regardless of which of them is the liar/truth-teller).

"The left road leads to the Truth-teller Tribe." - This statement rules out the possibility of them both being from the Truth-teller Tribe (1. is not possible), which means that the L e f t \boxed{Left} road is the correct road.

We don't actually need to know which native is from which tribe, but we can determine that A is the Truth-teller by the first statement.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Stephen Mellor
Jan 4, 2018

As at least one is truthful, there are 3 cases.

Case 1: A is true, B is true

A contradiction is caused as A says it's the left road and B says it's the right road, and then A says it's the right road.

Case 2: A is liar, B is true

A says it's the right road (A says left but is lying) and B then says it's the left road

Case 3: A is true, B is liar

A says it's the left road and B then says it's the left road and then A says it is the left road

As Case 3 is the only one which contains consistent information, it's the left road.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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