# Where’s my present?

sequel of: Which of my friends has a birthday today?
Hello. It's me again. Today is my birthday! So of course I met my friends today, along with a new friend that I made the other day. This new friend of mine is called Felicity. Unfortunately, they're up to it again, and it seems that they have recruited Felicity also.

To recap from last time, if one of my friends is lying today, everthing they say is false. No part of what they say is true. If not, then everthing they say is true, there is no falsity to be found in what they say.

Every year my friends all go out and buy me a present. This year, they have decided to hide it. I asked them each where it was, and this is what they each said to me.

Andrew:

between Cassie and Danielle, there is at least one liar. As a matter of fact, there is exactly one liar between them. The present is in one of these locations: the basement, carpark, closet, lounge room, meeting room or shed.

Benjamin:

There is at least one liar between Andrew and Cassie. Exactly one of them is a liar. We hid the present in the basement.

Cassie:

between Benjamin and Eric there is at least one liar. Exactly one of them is the liar, no more. Your present can be found in either the closet, lounge room or meeting room.

Danielle:

Cassie, Eric and Felicity are not all telling the truth, there is exactly one liar between them. We put the present in either the carpark or the closet.

Eric:

Your present is hidden in either the carpark, lounge room, meeting room or shed.

Felicity:

Your present is in either the basement, carpark, closet, meeting room, shed.

That's all they said. I need your help again! Who is telling the truth and who is lying? Where is my present? I haven't the faintest idea!

The present is in:

the meeting room

Any location mentioned is listed as a possibility by Andrew therefore:

either Andrew is telling the truth or no one is

A,B,C, and D all mention that there is at least one liar within some group, then say it is exactly one

if any of these are lies then everyone in that group would be a truth sayer, so there must be no more than one liar in any of these groups.

Because Benjamin said that the present could only be in the basement, if he is telling the truth then anyone who did not list the basement would be a liar

This would violate the rule of no more than one liar among the group C, E, and F (from Danielle's statement)

We now know that Andrew is telling the truth and Benjamin is lying

From this we can get the rest

Andrew - Truth
Benjamin - Lie
Cassie - Truth
Danielle - Lie
Eric - Truth
Felicity - Truth

The present is hidden in the

meeting room

and

Andrew, Cassie, Eric, and Felicity are telling the truth, while Benjamin and Danielle are lying.

How I solved it:

Assuming Benjamin is telling the truth leads to a contradiction. So Andrew and Cassie are both telling the truth. Then Danielle must be lying, which implies Eric and Felicity are telling the truth. Combining the assertions tells us the present is in the meeting room.