A satisfiability problem

[Sahir Shibley]

I got this in the mail yesterday. Its not too difficult but is a nice little puzzle that helps you to exercise your problem solving abilities.

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You are chief of protocol for the embassy ball. The crown prince instructs you either to invite Peru or Slovenia or exclude Qatar. The queen asks you to invite either Qatar or Romania. The king, in a spiteful mood, wants to snub either Romania or Peru or both. The prime minister calls to say if the Peruvian ambassador meets the Romanian amabassador a fistfight is bound to break out.Make a guest list that will satisfy the whims of the entire royal family and avoid an unpleasant incident at the ball?

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[This message has been edited by Sahir Shibley (edited June 07, 2001).]

[Paul Ralph]

Invite noone. Technically, that satisfies the requirements, but I have a sneaking suspicion it's not the answer you are looking for.
When you say OR do you mean either or (|) or exclusive OR (^)?
Paul R
[This message has been edited by Paul Ralph (edited June 07, 2001).]

[Cynthia Yao]

so based on your saying:
P peru
S slovenia
Q qatar
R romania
crown: P | S | ~Q
queen: Q | R | ~S
king ~R | ~P
minister: P xor R
only P xor R are a most condition, so you can only invite one of them. You can invite R or S or both.
did I understand it right?

[Sahir Shibley]

Paul,
No guests means no party. However I have modified the question to exclude that possibility. The queen's instruction is now to invite Qatar or Romania so you must invite one of them to make her happy.
Cynthia,
It does not matter if its | or ^. Because he is just telling you if you have one you cant have the other.

[This message has been edited by Sahir Shibley (edited June 07, 2001).]

[Paul Ralph]

I still don't get it. In particular, the prime minister's request makes the king's request redundant or vice versa. Is there supposed to be only one solution or do you have to invite the most possible? Again, could you clarify the "OR"?
Would the crown prince be OK with inviting Peru and Slovenia, for example? My best guess is 1. Peru and Qatar 2. Slovenia and Qatar 3. Slovenia and Romania
If you include the Queen's last request, that eliminates possibility 1 but I'm still missing something.
Paul R

[Richard Boren]

so based on your saying:
P peru
S slovenia
Q qatar
R romania
crown: P | S | ~Q
queen: Q | R | ~S
king ~R | ~P
minister: P xor R
Originally posted by Cynthia Yao

My attempt:

   crown: (P | S) | ~Q           (if P or S is not invited then exclude Q)
   queen: Q | R                  (invite either Q or R)
   king: (~R | ~P) | (~R && ~P)  (exclude R or P or both) 
   minister: P xor R             (if one is invited exclude the other)

Looks like Slovenia and Qatar are going to the ball to me.
Slovenia because noone said not to invite them. And Qatar because it would only be excluded if neither Slovenia or Pure were not invited; however, Slovenia was invited.
crown's happy Slovenia and Qatar are invited.
queen's happy Qatar is invited.
king's happy he gets to snub both Romania and Pure.
minister's happy because neither Romania or Pure is invited so there's no duking it out.

[Andrew Shafer]

Why not Peru and Qatar?
Prince is happy cause you invited Peru.
Queen is happy that you invited Qatar.
King got to snub Romania.
Prime Minister doesn't have to see any fights.
Or
Slovenia and Romania
Prince gets to invite Slovenia.
Queen gets to invite Romania.
King snubs Peru.
Minister no fighting.

No unique answer. . .seems like there must be something missing? What answer do you have Sahir?

[Junilu Lacar]

Invite China, Taiwan and the US and let the good times roll!
Slovenia and Romania, too.

[This message has been edited by JUNILU LACAR (edited June 07, 2001).]

[Eager Beaver]

Just invite ROMANIA and enjoy your party!

[Sahir Shibley]

Originally posted by Andrew Shafer:
No unique answer. . .seems like there must be something missing? What answer do you have Sahir?

Both are right. I did not say there was only one possible solution.

[Dave Vick]

Invite them all, then sit back and watch the fun!!

[Andrew Shafer]

Ahhh yeah, a pay-per-view. . .
In this corner, weighing in at a 130 lbs, the dignitary from Peru. ..