## Card Trick: Hard Brainteaser

I am a croupier who has three cards in a row (face down) on a table. 2 of them are aces, 1 is a joker. You don’t know the order.

**Problem:** With one question of a simple ‘yes’ or ‘no’ answer, determine with “absolute certainty” which of the three cards is an Ace.

But it’s not so easy-

if you point to any of the two Aces, the answer I will give you is always true. However, if you point to the Joker there’s a 50% chance that the answer is true, and a 50% chance that the answer is a lie.

*Thanks to Suineg for submitting this brainteaser*

(you can enter your answers below, will unmask Tuesday or Wednesday, thanks)

joe| Profile August 4th, 2008 - 6:03 amWith the 3 cards lying down in a row:

POINT TO THE FIRST CARD(LEFT CARD AS YOU LOOK AT IT) AND ASK

“Is the next card along an Ace?”

If the croupier says “yes” then choose the next card to the right, if not then choose the third one (most right as we look at it).

Why? Obviously if the one you are pointing at is an Ace then the croupier will tell you the truth and you will be correct.

If it is a Joker you are pointing at then the other two will be aces and it will not matter which one you pick but doing the above every time will make sure it is a certain choice no matter which card is first.

jae113| Profile August 4th, 2008 - 7:56 amYou could ask:

Could you lie to me about this card.

yash_opened| Profile August 4th, 2008 - 8:04 ami have a doubt…..if i point to any card , then will you give me an answer with respect to that card?…..if so, then the question i will ask you is this……while pointing to the middle card-

“is the right card an ace?”

if you answer yes then i will chose the left card(which will be an ace), or if you say no i will chose the right card.

i think this is what u wanted?

:-)

yash_opened| Profile August 4th, 2008 - 8:06 amsorry my mistake i ment if u say yes to my question i will chose the right card, otherwise the left……

sorry

falwan| Profile August 4th, 2008 - 8:29 amPut 2 cards together and 1 card alone…

Ask one question about the 2 cards:

Are these 2 card alike ?!!

If the answer is “Yes”, one of them is a guaranteed ace…

If the answer is “No”, the seperate card is a guaranteed ace.

Shawn| PUZZLE GRANDMASTER | Profile August 4th, 2008 - 10:03 amYou have to structure the yes/no question to the croupier in such a way that if he is lying, he must lie twice about the same question (lie about his lying), and thus tell the truth despite himself.

Choose a card and ask the croupier “If I asked you if this card is an ace, would your answer be yes?”

If it’s an ace, the croupier will truthfully say YES.

If the card is a joker, and the croupier decides to tell the truth, then he will say NO.

If the card is a joker, and the croupier is in the mood to lie, he will realize that had you asked if this card was an ace he would have lied and said YES. If he says YES in response to your question, he will be telling the truth. He must lie and say NO.

If the card is an ace, the croupier always answers YES

If the card is a joker, the croupier always answers NO

Bobo The Bear| PUZZLE MASTER | Profile August 4th, 2008 - 10:48 pmI’d try something like this:

Point to a card and say “If this card is a joker, will you answer this question ‘No’?”.

If you get a response (either “Yes” or “No”, then you’re pointing to an ace. But if you’re pointing to the joker, then the croupier can’t give you either response without creating a paradox. So, if all you get is a confused stare, the other cards are the aces.

doar823| Profile August 5th, 2008 - 3:08 amThe only thing I can come up with is to ask if each card is the joker 2 times…which ever one he says no on 1 of the 2 times is the joker. The rules say with just one question, but this is just one question asked multiple times.

marsyk| Profile August 5th, 2008 - 8:06 amHere are my thoughts.

Point to the first card and ask “is the middle card a joker”. In case of “yes” pick the last card, case of “no” pick the middle card.

Explanation:

There are three differents scenarios here (we dont differentiate between the aces):

1. E E J = NO

2. E J E = YES

3. J E E = 50% YES (lie), 50% NO (truth)

YES = J E E or E J E ; pick last card.

NO = J E E or E E J ; pick middle card.

Thats it folks,

Martin

marsyk| Profile August 5th, 2008 - 8:15 amOne more thing just to clarify: E = Ace, J = Joker.

HeadlessCow| Profile August 5th, 2008 - 10:17 amPoint to two cards and ask if the third card is an ace. You know that he will tell the truth since you are pointing to at least one ace. If yes, then choose the card you didn’t point to. If no, choose either of the cards you are pointing to.

Anastasia11| Profile August 5th, 2008 - 10:30 amPoint at one card and ask about another card “is this an ace?”

If yes then that card is an ace.

If no then the remaining card is an ace.

If the card I asked was an ace, then he has to tell the truth.

If the card I asked was the joker, then both of the other cards are aces.

michaelc| Profile August 5th, 2008 - 2:37 pmAh, very clever!

Point at one card and ask about another. I good question for a logic 101 final exam. One that I would have failed by the way…

suineg| PUZZLE MASTER | Profile August 6th, 2008 - 9:18 amGreat alternative answers, However only a few got the right logic to get this done; first I will explain why the double negation does not work and why other answer does not work.

Double nagation does not work because if you point the joker you have 50 % chance of lie or truth.

Example :If I asked you if this card is an ace, would your answer be yes?

your a pointing an ace the answer will be yes, cool

if you point the joker the answer could be yes or no,

because the croupier can lie or can tell the truth.

Other answers put together two cards, you can’t manipulate the cards, but if you could the croupier will be in a logic problem, should a tell a lie or a truth, the probability of truth rise but you have no absolute certanty.

Other arise the problem of paradoxes, not paradoxes there because the croupier response with truth or lie if you point a joker, is a congruent response.

Some use more than one question and thats not valid.

Joe, Yash_Opened and Anastasia11 got the right answer.

Explanation: The cards are 1,2,3 from left to right; the answer can be found pointing any card; If you point to 1 an is a JOKER does not matter the response the croupier gives you, the other two cards are ACES, so you EXCLUDE that option, the only thing that matter is the case if you are pointing an ACE, so you EXCLUDE a question about the card you are pointing because you are assuming is an ACE and ask if card 2 or 3(does not matter which one) is an ACE, if the answer is “yes” you choose that one if the answer is “no” choose the other one. this is based in a logic principle call mutual exclusion, cool.

suineg| PUZZLE MASTER | Profile August 6th, 2008 - 9:40 amShawn double negation is a cool answer because it almost kill the croupier choose of answering, you know I get that if he says yes he is telling the truth about his lie, I mean if he lies his response will be yes, so if you says he has to lie in a recursive way his yes would be the truth but he has to lie so you say no, but at the same time that would be truth, its hard jajajajajaja, so you has to assume that the lie is simple and direct with and “AND” so one of the premise is a lie no matter that the other one is a truth so could be a “yes” too, its hard to explain Shawn because you put that principle to his limits, but I think it would not work because you would have not reponse by your question, the croupier has to answer and he will answer by the “AND” rule I guess, just to clarify that answer that was a really complex one, cool.

suineg| PUZZLE MASTER | Profile August 6th, 2008 - 9:54 amjajaja sorry it has to be the OR rule only one of them has to be truth and a lie can be possible jajaj I get all fuzzy, man that was hard to clarify or to “obscure” jajaja does not know anymore Shawn.

Shawn| PUZZLE GRANDMASTER | Profile August 7th, 2008 - 3:32 pmI see, so the “trick” to your question is that you must point to a card, but ask the question about a different card. It is easy to read the problem statement and assume that the croupier will give a truthful answer about the card to which you are pointing, but that is not how the problem is stated. Clever.