Decide from the statements heard in the three rooms which ghost haunts each room.

Question

In an old mansion, three ghosts haunt three of the rooms: the library, the dining room, and the billiards room. The first ghost, Ebenezer, always tells the truth; the second, Jane, sometimes tells the truth; Gregory never tells the truth. Decide from the statements heard in the three rooms which ghost haunts each room.

Library: Ebenezer haunts the billiards room.

Dining room: Gregory's ghost is in the library.

Billiards: I am the spirit of Jane.

Answer 1

Suppose Gregory is in the library...

then Ebenezer MUST be in Dining room, which puts Jane in the BIlliards room.

This scenario is consistent with the other statements, since Ebenezer always

tells the truth. Jane is telling the truth in this instance.

Suppose Gregory is in the DIning room...

Then Ebenezer is in the Library and Jane in in the Billiards room, or VICE VERSA.

If Ebenezer is in the Library, then this scenario results in a contradiction, since

Ebenezer always tells the truth.

The other option is that Ebenezer is the billiards room and Jane is in the library.

This scenario also results in a contradiction, since Ebenezer always tell the truth.

Suppose Gregory is in the Billiards room...

then Ebenezer is in the Library and Jane is in the dining room OR vice versa.

Assuming the first of these two, leads to a contradiction, again as

Ebenezer always tells the truth. Then in this scenario, Jane is in the

library and Ebenezer is in the dining room. This scenario does not fit

either.

Gregory in the library, Ebenezer in the dining room, jane in the billiards room.