Braingle Lite



Five Cards

Category:Logic
Submitted By:Poker
Fun:*** (2.48)
Difficulty:**** (3.19)



I was playing a game of five card draw poker with a bunch of logicians. By the time we had finished bidding and were just about to reveal our cards, I was pretty confident I would win of the four of us remaining. I had three nines, some face card (I can't remember what suit or even whether it was a jack, queen, or king) and a four. (Or was it a five? I can't remember.)

I was even more sure when two of my opponents laid down their cards. One had a pair of fours and a pair of sevens, the other had a pair of twos and a pair of eights. My third opponent, however, laid down his five cards face down in a row. He said, "I have a straight, and the cards are, from lowest to highest: a ten, a jack, a queen, a king, and an ace. I have at least one card of each of the four suits: clubs, spades, hearts, and diamonds. I am fairly certain that this is the winning hand, but I'm feeling generous today, and I will give a third of the pot to whoever can determine which suit I have two cards of.

Now I know you can't figure it out without some clues. Here they are:

1. The king is next to at least one diamond.
2. The queen is next to exactly one heart.
3. The jack is next to at least one spade, but is not next to any hearts.
4. The ten is next to at least one club.
5. The ace does not border any black cards, nor does it border any diamonds.
6. My two cards of the same suit are not next to each other.
7. Of the ten possible pairings of cards, only one pair, when removed, leaves three cards in ascending order from left to right.
8. My ace is not the card on the far left."

There was a minute's silence. One of the other logicians said, "I give up! There's no way to figure that out!"
The other agreed. But I didn't. I had just figured out which suit he had two of.

Which suit is it?

Show Hint Show Answer



Comments on this teaser


Posted by Poker06/17/04
My first teaser! :D

Posted by jmcleod06/17/04
Wow! that was well thought out and well done.

Posted by fishmed06/18/04
Very good. :)

Posted by doggyxp06/18/04
This reminds me of the Potions "Task" in Harry Potter and the Sorcerer's/Philosopher's Stone that Hermione solved on the way to get the Stone.

Posted by Poker06/24/04
In what way?

Posted by Mogmatt1607/02/04
wow, good job Poker. Rarely is someone's first teaser such a good one!

Posted by Poker07/02/04
Thanks, Mog! It's one I created some time ago. Glad you like it! Others I have made, on the other hand, aren't quite as good.

Posted by cnmne07/11/04
Well done, especially in determining the suits for the king, queen, and ace. I do have one problem with the teaser. The second statement about the queen being next to exactly one heart led me to believe that the queen had to be on either end, especially since other statements used the phrase 'next to at least'.

Posted by Poker07/14/04
I said next to exactly one heart. I didn't say about any of the other suits.

Posted by Poker07/23/04
Let me explain it to you again. The card on the left end borders a card of one suit - call it suit A. The card on the right end borders another suit - call it suit B. Suits A and B could be the same suit, but that's beside the point. The point is, the card in the middle borders a card of suit A and a card of suit B, since there are five cards. The card on the left will be listed as bordering suit A, the card on the right will be listed as bordering suit B, and the card in the center will be listed as bordering either suit A or suit B. So one of suits A and B will be listed twice. The only suit listed as bordering two cards is hearts - and it borders the ace and the queen. The ace can't be on the left side, nor can it be in the center (the card on the end that is not the queen borders something other than hearts), so it must be on the right, with the queen in the center. Which explanation do you prefer - this one or the one in the answer?

Posted by i_am_hated03/18/05
woah

Posted by Sarcastique03/19/05
:-? I couldn't answer it if you would pay me. It was cool though 8)

Posted by whaleycm03/30/05
Line 7 really threw me off. I never quite understood what that meant.

Posted by koolkat5703/31/05
:o

Posted by Poker04/18/05
Sorry, but your "second answer" doesn't meet the conditions of clue 7.

Posted by DMS101US04/27/05
I came up with the answer TJQKA DCSHD Is this one wrong? the ONE and ONLY Stan D Man :wink:

Posted by darthforman05/11/05
:-? I'm lost, I guess this is why the only card games I play is solitare and battle and BS. :-? :oops:

Posted by Poker05/18/05
Once again, clue 7 is not met.

Posted by cdrock05/30/05
wow poker, that was really hard, thats the only logic problem that I tried that I couldn't figure out. :-?

Posted by schatzy22808/27/05
excellent 8) i didn't get it in my self imposed 2 minutes, so when i saw how you worked the clues i'm glad i gave up,,,very well done :wink: :D

Posted by schatzy22808/27/05
wow,,i didn't notice how old this one was :lol: ,,i was just searching the ones rated most difficult :roll:

Posted by NomadShadow10/27/05
A good one, and it's not easy; it took me 15 minutes to solve it. Keep up the good work

Posted by hawkinsunc12/15/05
Your Clue #7 is confusing. The way you make it sound, there can be ONLY ONE sequence of cards that will satisfy Clue #7, when, in actuality, there are other sequences that will fit this clue.

Posted by mercenary00704/01/06
that was a very good teaser... yeah I know that I'm late to seeing it but I just joined this site not too long ago... I nearly got it out but what got me was the last part where you had to review the cards that were in your hand and not only the cards in ur opponents hand. VERY GOOD 8)

Posted by flowergirl121907/14/07
E-Z But very fun and well thought out

Posted by roaddevil08/12/07
No way to determine the order of the cards, why couldn't they be in order?

Posted by AndrewWalker07/07/08
easy for me :D

Posted by Jota10/08/08
The way I see it, there are five different possible answers: K J Q 10 A S D C H S S D C H C S D S H C C D S H C S D C H D I believe all five of those options satisfy the conditions stated in the clue. So he could have two clubs or two spades or two diamonds. Also, the problem states that with regards to the face card in your hand you "can't remember what suit or even whether it was a jack, queen, or king". This to me means that the identity of the face card is unknown to you when trying to reason which suit appears twice in the hand. So I don't see how you could figure out that it was a King or which suit it is without guessing.

Posted by javaguru12/28/08
Great teaser! Took a while to get it. There are 24 possible orders for the cards to meet clues 7 & 8: TKAQJ TAQKJ TAKJQ JKATQ JKTAQ JKAQT JKQTA JKQAT JAQKT JAQTK QKATJ QKAJT QKTAJ QKJTA QKJAT QTJAK QTAJK QATJK KTQAJ KJQTA KTAJQ KQTJA KJQAT KATJQ Of these only two can satisy the rest of the conditions: JKQTA KJQTA For JKQTA the pattern must be XSXHX. There are six ways to complete this pattern to satisfy the conditions: JKQTA DSDHC 2D CSDHC 2C HSDHC 2H DSCHD 2D DSCHC 2C DSCHS 2S There is no face card that the player can hold that will produce a single answer. (Jack of diamonds allows either clubs or hearts.) For KJQTA the pattern must be XDXHX. There are five ways to complete this pattern to satisfy the conditions: KJQTA CDSHC 2C SDCHC 2C SDSHC 2S SDCHD 2D SDCHS 2S Only the king of spades reduces this to a single possibility, which is of course clubs. 8)

Posted by javaguru12/28/08
I didn't make it clear in my previous comment that having the king of spades in my hand would also eliminate all of the JKQTA combinations since they all require the king of spades.

Posted by G-RAN-IT05/10/09
Just joined and this is one of my first teasers... You say the answer is: KJQTA CDSHC How does this satisfy the seventh citeria: 7. Of the ten possible pairings of cards, only one pair, when removed, leaves three cards in ascending order from left to right After removing the pair of suited cards (the only pairing) it leaves you with: JQT How are those three cards in ascending order from left to right ? ascending order would be TJQ ! The answer I came up with is: TJQKA SCDHS After a quick double-check it seems to satisfy all criteria. Not to mention most poker players lay down their straights in ASCENDING SEQUENTIAL ORDER ! With that rational taken into consideration I think that is the simplest answer and therefore the best answer. I didnt bother to look for a second answer for that same reason - the simplest answer is the best answer. Well, that and I just didn't want to spend any more time on this...

Posted by javaguru05/12/09
G-RAN-IT: Nothing in the seventh criteria restricts the pairing of cards removed to be of the same suit. So there are (as the criteria states) ten possible pairings. The only pair of cards that can be removed from KJQTA to leave ascending cards is KT, leaving JQA. ANY pair of cards removed from your solution leaves three cards in ascending order. :(

Posted by G-RAN-IT05/12/09
That last comment didn't carify anything... Your statement doesn't take into consideration that the cards are to be ordered: The only pair of cards that can be removed from KJQTA to leave ascending cards is KT, leaving JQA. JQA are not an order. JQK would be an order. and if ANY TWO cards can be removed why is it referred to as a pair. A pair by definition is: Two corresponding persons or items, similar in form or function and matched or associated. how are KT similar or associated ? they are about as similar as ANY two cards are in the deck, common only in that they are both cards in a deck. I still stand by my last comment - the best answer is the simplest and I believe I found that. Not to mention I don't believe the original answer is even correct - based partially on the fact that a pair needs to have something in common such as a suit, which I believe was the main factor that we were after - and it just so happens that there are only 10 possibilities of suited pairs. I could go on but i won't...

Posted by javaguru05/14/09
A pair of cards, a pair of ducks, a pair of coins...doesn't seem all that semantically challenging to me to have a pair of cards. :-? If two of the cards had the same rank, then the wording (which could have been better) would be wrong because with cards, a pair means the same rank. Also, "ascending order" does not say "consecutive ascending order". You're reading more into the words than is there. Your solution clearly doesn't meet the criteria.




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