Logical Problem

College Confidential Community
1

<p>Hey all! I found a really hard logical problem on the internet. It took me about 10 mins to solve it. How long would it take the rest of the CC?:)</p>

<p>Students X, Y and Z are good at logical reasoning. They already know that the drawer has the following 16
playing cards:</p>

<p>Heart (:heart:): A​:heart:、Q​:heart:、4​:heart:
Spade (:spades:): J​:spades:、8​:spades:、4​:spades:、2​:spades:、7​:spades:、3​:spades:
Club (:clubs:): K​:clubs:、Q​:clubs:、5​:clubs:、4​:clubs:、6​:clubs:
Diamond (:diamonds:): A​:diamonds:、5​:diamonds:</p>

<p>Teacher W now picks one card out of these 16 cards from the drawer without X, Y and Z seeing it.
Then W tells the rank of this card (i.e., A, 2, 3, 4, 5, 6, 7, 8, J, Q, or K) to Y and the suit of this card
(i.e., Heart, Spade, Club, or Diamond) to Z. Then he asks Y and Z whether each of them can infer
what this card is just from the partial information they each have. At this point, X hears the following
conversation between Y and Z:</p>

<p>Y: I don’t know what this card is.
Z: I know that you don’t know what this card is.
Y: Now I know what this card is.
Z: Now I also know what this card is.</p>

<p>After hearing the above conversation and thinking for a while, X also knows what this card is.</p>

<p>What is this card? Justify your answer.</p>

2

<p>No one gets it? Or you guys just don’t bother to read it. :o</p>

3

<p>It has to be the 5 of diamonds.</p>

<p>Reasoning:
Y, who was told the rank, doesn’t know what the card is. That immediately rules out the Jack of Spades, 8 of Spades, 2 of Spades, 7 of Spades, 3 of Spades, King of Clubs, and 6 of Clubs.</p>

<p>Since Z, who was told only the suit, knew that Y didn’t know what the card was, we can rule out all the spades and clubs. </p>

<p>So now we’re left with Ace of Hearts, Queen of Hearts, 4 of Hearts, Ace of Diamonds, and 5 of Diamonds.</p>

<p>After hearing that Z knew that Y didn’t know what the card was, Y was able tell which card it was. This rules out the Ace.</p>

<p>Now, we’re left with Queen of Hearts, 4 of Hearts, and 5 of Diamonds.</p>

<p>After being told by Y that he knew what the card was, Z also knew what the card was.</p>

<p>I think this is the tricky part.</p>

<p>Z couldn’t have known what the card was at this point unless he was told that the suit was Diamonds. Therefore, the card has to be the 5 of diamonds.</p>

4

<p>Nicely done! I guess its too easy for you geniuses.</p>