Black Vienna 1.0 - Solution
There are 27 cards in Black Vienna, each representing an individual and these are labeled A through Z plus Ö. Three of these are secretly put aside and they form the legendary criminal ring Black Vienna. The remaining 24 cards are dealt amongst all the players. Your task is to deduce which three people form Black Vienna.
To deduce the outcome, players question each other by playing investigation cards. Each such card contains three different letters. When it is a player's turn he puts one of the available investigation cards in front of any other player. That player must then place one chip on the card for each matching person card he holds in his hand; if he holds no listed suspects, he places no chips. (e.g. If a player receives the BLM card and has the letter B in his hand but not L or M, he must put exactly one chip on the card.)
The current situation:
It's a three-player game. The cards in your hand are: B C D E O T U V
The information you've received so far is as follows (the numbers are the number of chips that player placed on that particular investigation card):
There are currently three available investigation cards:
It's your turn. Which investigation card should you give to which player so that, regardless of his answer, you are able to deduce the members of Black Vienna?
The key is in the two investigation cards: KPW & APQ
Since neither you nor Magnus have any of these 5 suspects, and Marko has at most 2, Black Vienna must be comprised of some subset of A, K, P, Q, W.
Does Marko's hand contain the P card? Assume that it does. Therefore Marko(KPW) = 1 implies that both K & W are in Black Vienna. However, Marko(APQ) = 1 implies that both A & Q are also in Black Vienna. This is obviously impossible since Black Vienna may contain only three cards. Therefore our assumption that Marko's hand contains P must be incorrect and therefore P must be in Black Vienna (since we now know that it is not in any player's hand).
Now using Marko(KPW) = 1 implies that either K or W is in Black Vienna.Also, Marko(APQ) = 1 implies that either A or Q is in Black Vienna.
Let's first tackle the question of whether K or W is in in Black Vienna.
- Magnus(CSX) = 2 implies that Magnus has S & X (since you have C in your hand).
- Marko(GPX) = 1 implies that Marko has G (since Magnus has X and P is in Black Vienna).
- Marko(EGW) = 1 implies that Marko does NOT have W (since we now that he does have G).
Therefore W is in Black Vienna since neither you nor Magnus nor Marko has it in hand.
Now we need only figure out whether A or Q is in Marko's hand. By handing him BQT we can determine this because you have B & T in your hand. If he answers 1 then he must have Q in hand and by our previous logic, A must be in Black Vienna. If he answers 0 then Q must be in Black Vienna since it is not in any player's hand.
Congratulations to Nick Berg whose name was drawn from all the correct entries. Nick will receive an item of choice for the Fabulous Prize Vault!