Cards Trick

· · math cp tutorial

A trick between 2 magicians, exposing the math behind

This is a communicational technique, in pocker cards (Baloot).

Idea

  • Give $A$ 5 cards (arbitiraly/randomly)
  • He will throw some card to the garbage, and give the cards to $B$
  • $B$ will know the card in the grabage

Explaination

Steps for $A$:

  • Find two cards with same type (♥/♦/♣/♠), and will meet formula $C_2 = (C_1 + N) \text{ mod } 13$ such that $1 \leq N \leq 6$
  • Throw card $C_2$ to the grabage
  • Put card $C_1$ to the first
  • The rest of the three cards, order then in $N$-th lexicographical order

Steps for $B$:

  • The type of the card in the garbage is the same as the first card
  • Calculate the lexicographical order of the three cards
  • The card in the garbage is $C_1 + N \text{ mod } 13$

Implementation

Here is a C++ code that does this