Cardopolis

OPEN AND SHUT CASE

This item was previously published in New Talon number 3. It was inspired by Jack Yates’ effect Clue from his book Clue and other Miracles. It can be presented as a murder mystery game. But my main reason for describing it here is to highlight the method, which might interest anyone familiar with those logic puzzles featuring liars and truth-tellers.

Effect: The performer invites six spectators play the part of suspects in a game of murder. One of them is a murderer but only the murderer knows that. Three of them are compulsive liars. Fortunately the other three always tell the truth. The task of the performer is to navigate his way through this maze of deceit and correctly identify the murderer. Naturally, he always does.

Method: I’ll just describe the bare bones of the method. If you like the idea, you’ll find ways of dressing it up and devising an entertaining presentation. To perform the trick you’ll need six blank cards. On three of them write the word LIAR. On the other three write the word TRUTH. You’ll also need a bag (cloth or paper), five white counters and one black counter.

Arrange the cards so that they alternate TRUTH, LIAR, TRUTH, LIAR, TRUTH, LIAR. Put the counters in the bag. Get yourself six volunteers and you are all ready to go.

Bring out the cards. Display a couple of them to show that some of them bear the word LIAR while others contain the word TRUTH. Don’t mention anything about there being an even distribution of LIAR and TRUTH. And don’t reveal the fact that the words alternate. You may indulge in a brief false shuffle but if you do make it a casual looking one.

Arrange your six volunteers in a line. Get the attention of the first volunteer and show him how to cut the cards and complete the cut. Make sure he understands the procedure and then hand him the cards face down. Tell him to put the cards behind his back and give the cards a cut. And then another one. As he does this take out the cloth bag.

When he’s finished cutting the cards, ask him to take the top card of the packet and pass the remainder of the cards to the next volunteer. The second volunteer takes the new top card of the packet before passing the packet on to the third volunteer. Each volunteer takes a card from the top and then passes the cards on until all six volunteers have a card each.

Tell the volunteers to take a peek at the card they are holding. The cards tell them which roles they should play. They will either be a truth teller or a liar. You must really hammer it home that if the volunteer is to play the part of a liar he must lie all the time. It doesn’t matter what he says as long as it is a lie. On the other hand good liars tell lies that can be believed. The opposite applies to the truth-tellers. You cannot overemphasise this. So make it part of your presentation, talking about the compulsive liars and truth-tellers that are part of this story.

Look away while the volunteers peek at their cards. They can put the cards away when they’ve noted their role in the game. Explain that each volunteer will be asked to reach into the bag and pull out one of the counters. Whoever draws the black counter will play the part of the murderer.

The bag is passed from one volunteer to another so that they can draw counters. They hold the counters in their closed fists. Then, when everyone has one, you turn away and the volunteers look at the counters noting whether or not they have the black one. No one allows anyone else to see which counter they have. Only the person with the black counter knows that he or she will play the role of the murderer in this game. The counters are placed out of sight with the cards.

Let’s review the situation. You can’t possibly know who the liars are and who the truth-tellers are. And there is no way for you to know who chose the black counter so you don’t know who the murderer is either. And yet that is precisely what you are going to reveal. And you can do it with one simple question to each volunteer.

Example 1: Let’s assume that the third volunteer in the line of six is the murderer. Let’s also assume that because of the prearrangement of the cards the line alternates TLTLTL, which makes the third volunteer a truth-teller. If you ask each volunteer, “Do you know who the murderer is?” you would get the following yes or no answers: No, Yes, Yes, Yes, No, Yes.

You can see a pattern emerge. There is a block of three ‘yes’ answers. The middle volunteer of any block of three similar answers (in this case it happens to be ‘yes’) will be the murderer. It always works. If the alternation of the cards had made the third person in the line a liar, then you would have a block of three ‘no’ answers and the middle volunteer of this block would be the murderer.

You can also deduce that if the block of three answers is ‘yes’ then the murderer is a truth-teller. If ‘no,’ then the murder is a liar.

Example 2: The block of three might be split by the end of the line but if you are familiar with any kind of stack you will still be able to pick out the block of three. For instance, if the first volunteer in the row is the murderer and the row alternates LTLTLT then the answers to your question will be No, No, Yes, No, Yes, No. The block of three is split but it should be clear that the first volunteer is the middle one of the split block.

By asking only one question of each spectator you can instantly identify the murderer. When presenting the effect it’s best not to ask the key question, ‘Do you know who the murderer is?’ immediately. Instead, give the volunteers time to get into their roles of liars and truth-tellers. If you are presenting this as a murder mystery party you might ask them to think about what they had for dinner. Or to drink. And warn them that in a moment you will ask them a question and that the truth-tellers will always tell the truth but the liars will always lie. Then make good on your promise by asking what each of them what they had for dinner. Make light of the various answers you receive.

You now ask each of them the key question. But do it at random. Don’t just go along the line. Remember who gave what answer. Spot the block of three and deduce who the murderer is and whether they told the truth or a lie. In the finale you first reveal whether the murderer is a liar (a double sin) or a truth-teller. And then go on to identify him or her. It’s as simple as that but as with everything it will only be as entertaining as your presentation. So dress the routine as best you can.

Notes: Although you are looking for a block of three similar answers you can, in some circumstances, identify the murderer from questioning as few as three volunteers. Take Example 2. You only need answers from the first three volunteers (No, No, Yes) to tell you that the first volunteer is the murderer. That’s because if you hit two similar answers you are already in the block of three. Now you can ask the rest of the group completely different questions. It’ll confuse any clever puzzle-savvy folk trying to work out the method.

Need I mention that once you understand the basic principle you can improvise using a deck of playing cards and other items rather than having specially made cards, counters and bag? It makes a good impromptu party trick. Provided everyone is sober!