Famous magicians Dylan Rhodes and Daniel Atlas performed an exhilarating magic trick in my last birthday party. Since, it was my birthday, Rhodes asked me to shuffle a new deck and pick any five cards out of it. I took out the cards as asked, looked at them and then showed all five cards to Rhodes. Rhodes then gave four cards to Daniel and the remaining fifth card to me. Daniel looked at the four cards for about ten seconds and then he told me what card I was holding.
Surprise, Surprise! He was right!
It was quite surprising to me at that time, but when I reached back home, I was able to crack the trick behind the magic.
The five cards must contain at least one card of the same suit.
Let’s assume Rhodes placed one of the two cards of the same suit at the end and the second card was given to Daniel.
In that case, Daniel will know the suit of the card.
Now the real question is how Rhodes made sure that Daniel also knows the number of the card.
Daniel got four cards and one of them will determine the suit, so we are left with 3 cards.
3 cards can be arranged in 3! ways i.e. 6 ways but our card numbers can vary from 1 to 13.
Since we have two cards of the same suit we will make sure that we don’t pick the King (13). This leaves us with 12 numbers.
We can also distinguish card from upside down position, therefore, we now have 6 * 2 ways to arrange these card.
“TADA…. We cracked the magic trick”.
Let us assume that the smallest card is C1U (upwards position) and C1D (downwards position). Similarly, we have C2U, C2D, C3U and C3D
According to that, the 12 possible arrangements are:
C1U C2U C3U => NUMBER 1
C1U C3U C2U => NUMBER 2
C2U C1U C3U => NUMBER 3
C2U C3U C1U => NUMBER 4
C3U C1U C2U => NUMBER 5
C3U C2U C1U => NUMBER 6
C1D C2D C3D => NDMBER 7
C1D C3D C2D => NDMBER 8
C2D C1D C3D => NDMBER 9
C2D C3D C1D => NDMBER 10
C3D C1D C2D => NDMBER 11
C3D C2D C1D => NDMBER 12
Please note that king (number 13) is not possible as discussed already.