The Best Ever Card Trick

Logic Level 2

A magician randomly picked Sam from the audience to perform his next act. After Sam get's on stage, \(\ldots\)

Magician: From this ordinary deck of cards, please draw five cards. Choose them as you please, but do not show them to me.

(Sam chooses five cards)

Magician: Perfect! Now, show them to my lovely assistant.

(Sam shows cards to the assistant)

Magician: Now, my kind assistant will give me four of them.

(Assistant gives the cards one by one to the magician)

Magician: Okay, here we go, the \(\color{black}{7\spadesuit}\), then the \(\color{red}{Q\heartsuit}\), the \(\color{black}{8\clubsuit}\) and the \(\color{red}{3\diamondsuit}\). And dear gentleman, is the hidden card \(\color{red}{K\spadesuit}\)?

Sam: Yes, it is!

(Applause)

The audience is abuzz, trying to figure out what happened. There are 52 - 4 = 48 cards left in the deck. How did the magician figure out which card to announce? Clearly, the assistant must be in on the trick. But what information could the assistant provide other than changing the order that the cards are displayed?

Is it possible for the assistant to convey the information of the fifth card Sam chose just by changing the order in which the other cards are passed on?

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