Question

David Blaine and Dynamo performed together in our college fest. I was chosen to be performed a card trick on. Blaine asked me to shuffle a deck of cards and when I was done, he asked me to pick any five cards. I did as he had asked and showed my selected cards to Blaine.

Out of those five cards, he gave four to Dynamo and one back to me. Upon looking at those four cards, he was able to deduce the card I was holding.

I was shocked. It was brilliant. But when I was returning back home, I thought about it and was able to crack the trick.

Do you know how they did it?

Answer 1

It is plain and simple that in five cards, two cards must be of the same suit.

What Blaine did was place one of those cards at the end and gave the other cards to Dynamo. Now, Dynamo knows the suit of the card.

So how did Blaine ensure that Dynamo knows the number on the card as well?

Since one of the cards determines the suit, we have 3 cards. If you know a little about permutations, the 3 cards can be arranged in 3! ways i.e. 6 ways. If we make sure that the King is not picked, it leaves us with just 12 numbers.

The cards can be distinguished from upside down position, which gives us 6*2 ways of arranging the cards.

Let us denote the smallest card as X1U for upward position and X1D for the downward position. We can go up from there as X2U, X2D, X3U, X3D and so on.
The possible 12 arrangements will now be
X1U X2U X3U => Card No. 1
X1U X3U X2U => Card No. 2
X2U X1U X3U => Card No. 3
X2U X3U X1U => Card No. 4
X3U X1U X2U => Card No. 5
X3U X2U X1U => Card No. 6
X1D X2D X3D => Card No. 7
X1D X3D X2D => Card No. 8
X2D X1D X3D => Card No. 9
X2D X3D X1D => Card No. 10
X3D X1D X2D => Card No. 11
X3D X2D X1D => Card No. 12