What’s My Card?
A student is given five random cards from a standard deck of 52 cards. He must choose four cards to reveal to his professor and the order in which to reveal them; his goal is to reveal four cards in such a way that the professor knows what the fifth hidden card is. How does he do this?
Communicated by Jeff Miller.
can i use binary no pattern
if yes then can i put all those 4 card face up or down
sadly cannot put in different spots on the table. imagine there are four
rectangles and must place cards in that…. it can be done –s
NOTE: the email address you gave me doesn’t work, email me at [email protected]
use binary pattern and arrage all four card to represent corespondant the 5th card
that is from 0001 (1) to 1101 (13) face up=1 and face doun represent 0
for color of card top edge of the table= red
little lower=spade
center of table=dimond
bottom edge of table =club
all face up
no timme delay
no placing at angles…
Do the cards all have to be face up? Can they be put down in different positions in the row of cards in a different order? I think I have something that works if you’re allowed to convey information by putting the second card into the third slot instead of the second slot, etc.
Glad to hear!
Glad to hear. //s
i love this website!!!!!!!!!
Email to you bounced. Please email me directly at sjm1 AT williams.edu
Solution please?
sure — sjm1 AT williams.edu
Would you please send solution to this puzzle? Thank You, Patrick
email me: sjm1 AT williams.edu
I’m thinking that a card would be 1 to 13 (J=11, Q=12, K=13). Having four binary places can cover up to 15. But how can I make a card represent 0 or 1? Am I on the right track?
ok
solution please 🙁
sergio: email me at sjm1 AT williams.edu to discuss
not sure what 1 means — you can email me at sjm1 AT williams.edu
1
I wanted to use 4! + 4 + 4! = 52 but couldn’t get that to work — emailed you a hint (sjm1 AT williams.edu)
yes, every situation (sjm1 AT williams.edu)
Assuming the hidden card is the/a repeated suit, is it possible to do the “trick” with either card hidden, or might there be a way to do it with just one of the cards hidden? In other words, will the trick work for EVERY situation?
So if we number all cards from 1-52, and if we always are dealt at least one card from 1-24, we can set that card as the fifth and use the other four cards to represent its number (4! arrangements of their numbers). But can you give me a hint as to how you would deal with getting all five cards >24? Or am I going about this wrong? I know this method doesn’t use all the possible information, but I’m not coming up with another way after about 30 minutes thinking about it
no — you can do it wi’out orientation
using only the order of the four cards gives half the required information.
can I use the orientation of the fifth card (e.g holding it horizontally or vertically) to convey the missing “bit” of information?
Mike L: you’re on the right path. The problem is that you can’t control how the cards are put on the table, only their order. your friend walks in after the cards are all laid down, face up, same orientation. you only get to choose the order. email me at sjm1 AT williams.edu to chat more //s
Mike L: not posting as this gives away a lot. Email me at sjm1 AT williams.edu — you’re very close, but you are using more info than you are allowed. The person coming in doesn’t know the order in which the cards were placed, and the four cards must go in four specific slots with specific orientations, so no way to use that to encode info.
you can do it without doing a trick like this. in other words, you tell ME what order your want the card to be placed and I’ll place them, so no signals through delays, spacing….
You lay them out with the correct spacing in between… if you have a 2,5,7,8,J…. You leave 2 card slots between 2 and 5, 2 slots between 2 and 8, and 2 between 8 and J. Then you point to the slot before the 8 and they figure it out.
I’ll send a hint first //s
Can you please send me the solution to this 5 card trick? I have tried about everything I can think of.
possible! email sjm1 AT williams.edu for a hint ..s
not possible
is he allowed to discuss a strategy before hand?
sure /s
Can I have the answer please?
if you need to do that, sure — however, it’s possible to do it by saying there are 4 boxes: [] [] [] []. you first put a card in box 1, then box 2, ….
Do you get to pick the order in which you lay them down? In other words, can I lay card number 1, then card 2 to its right, then card 3 to the left of those two, etc.? Or do I have to convey the final card simply with the order of the first four?
absolutely!
can you work out different things with the teacher before you do it
Email me at sjm1 AT williams.edu for a hint. //s
Confused
I don’t see how this allows the other person to get the hand as he can’t say what the hand is. /s
Could he organize them by the poker hand he holds and reveal what his hand is, eg “full house” while also organizing by increasing or decreasing numbers? If I’m wrong, please email me the solution. Thanks.
sure, sent ..s
i’d love the solution
You’re on the right track. The problem is you have to put down the other four cleanly. No rotation, all facing the same way. You control the order of the four cards, but that’s it.
You find two cards that share the same suit, since there is 5 cards atleast 2 will have to have the same suit. You will use one of these cards as the card you want the professor to guess for.. You take the other 4 cards, put them face down on a table and spell out the number that is the card the professor is trying to guess. 2 for 2, 9 for 9, K for king, etc. Leave the card with the same suit face up while the other 3 stay down and he should be able to guess the card. Am I right?
Let me try explaining the problem again. You are given 5 cards, say 2hearts, 5spades, 7diamonds, 8diamonds, Qclubs. You get to choose one of the five to keep hidden, and then place the other four down in such a way that your partner can glance down and deduce what the missing card is. You can’t ‘clue’ him in by things such as the angle the card makes with the table…..
2, 4, 6, 8? the next card would be ten…..so he would go by every 2…..unless i dont get the question…
but then he’s always showing the same thing…. email me at [email protected] to chat more.
he should show them from lowest to highest, in order to show some kind of pattern
You’re on a possibly right track, but the question is can you make it rigorous and work? There is a very simple way to do it where you ALWAYS put the cards down in a line, and thus don’t use 2-dimensions….
Isn’t that the soln? I mean, you are saying that you can arrange with your professor positions on the table to represent operators (next to means add, on top of means multiply, etc). So he arranges these four operators and a way to show suit (which also shouldn’t be that hard) and also a way to say “this card isn’t used” (just put them off to the side) and the question becomes “given four random numbers between 1 and 14, is it possible to arrange some of them and put operators between them so that it totals a different random number between 1 and 14?” That, I believe, is yes. I have not given exact arrangements because that is for the student and the professor to decide what is easiest for them.
email me at [email protected] for hints / solns
Nooooo its toooooooo hard
yes
Can the student see the five cards?
sure ..s
sir please send me the solution
it’s possible — email me if you want a hint ([email protected])
Impossible
Sure: the way you place the cards on the table can be used to represent numbers. You can also assign each card a number, and thus just need to ‘add’ or ‘subtract’ from a certain card. If you want another hint, let me know. /s
Could you give a hint?
And from Shane’s question, can I assume from the way you answered him that the student and professor did work out a strategy beforehand?
Thanks.
I’m at a liberal arts college. We’re all about encouraging student / faculty interaction. We actually meet for dinner and a Red Sox game and discuss the details in Fenway Park.
Is it assumed that the professor and student can not work out a strategy in advance? Or can they talk first?
Did you get my email?
Not sure what ‘how come’ means. Please email me at sjm1 AT williams.edu.
how come??
Done. If you didn’t get it let me know. //s