word problem

Question

To remind himself of where he buried his treasure, a pirate made this map. He made two of the statements true and one statement false to confuse his enemies in case they captured the map. How will the pirate know where he buried his treasure.

Three statements are:

1: The treasure is not on this island

2: The treasure is not on the island to the northwest.

3: The treasure is buried here.

Answer 1

Let us test the 3 in turn:

 

Let (1) be false, and (2) and (3) be true.  If (1) is false then the treasure is on this island.  This is logically compatible with (2) and (3) being true.

 

Let (2) be false, and (1) and (3) be true.  If (2) is false, then the treasure is on the island to the northwest.  This is logically compatible with (1) being true, but not with (3) being true.

 

Let (3) be false, and (1) and (2) be true.  If (3) is false, then the treasure is not buried here.  This is logically compatible with (1) being true, but there is not enough information to say if it is compatible or not with (2) being true, unless this island and the island to the northwest are the only possible burial places.  I assume they are.  If so, then (3) being false is logically incompatible with (2) being true.

 

In summary, only (1) false with (2) and (3) true are logically compatible, so the treasure must be on this island.