magic show

In a magic show, magician performed the following trick.

The magician left the room. The assistant handed over a standard deck of 52 cards to someone in the audience. The audience member chose any five cards from the deck and handed them to the assistant.

The assistant then selected one of those cards which he concealed from the magician, and displayed the other four cards side-by-side on a table.

The magician then entered the room, examined only the four displayed cards, and told the audience what the concealed card was.

Everyone was impressed.

But do u know what the logic was behind the trick

Might be the fifth card was changed by the assistant secretly to a card which the magician knew.???

It is the famous problem of combinatorics
we have 5 card in hand and we have to guess 1 card by having a look on 4 cards.
now we need to guess to thing color of the suit and number of card

Now by peigon-hole principle atleast 2 out of 5 cards should be of same suit. These 2 cards are of our use ,1 of these cards will be given first so that suit of the card to be guessed is known to us by 1st card. 1st job done
Now by 3 cards we need to guess 1 card. Make a circular arrangement of A to K
.............A
......2...........3
....4....................5
..6............................7
....8......................9
......10...........J
..........Q...K
Now maximum distance b/w any 2 cards is 6 and also 3 cards can be arranged by 3!=6 ways.
1st card which u've seen to know the suit should be such that other card can be reached from it by moving maximum 6 steps in this circle clockwise
Now you have to arrange those 3 cards in such a way that any of the number from 1-6 can be made and by adding that number of steps into first card number gives u the number of 5th card.
Now give priority to all cards and suits
heart > diamond > club > spade
and A < 2 < 3..........J < Q < K
hence, A(heart) < 2(heart) <......K(heart) < A(diamond) <............< K(spade)
now name those 3 cards small(S) ,medium(M) and large(L) according to the priority
now, arrange those 3 cards into following manner to get number from 1 to 6
SML-1
SLM-2
MSL-3
MLS-4
LSM-5
LMS-6
its done..
the assistant has arranged the cards into 1 of the above manner and the magician did the simple job >>
suit of 5th card=suit of first card
number of 5th card=no. of 1st card + number(steps) generated by 3 cards( in order)
u can also do this but u need to practice at least 20 times for perfection as i did.

the trick seems to work...

cool ans