Cards Trick

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