Magic & Math with Cards

Lecture 52 · Performance

Four cards name the fifth

Video in production

This lecture is still face down. Its script is written; filming and animation are under way.

Meanwhile, play the trick

What you will learn

Perform and explain the complete Fitch Cheney protocol for any five distinct ordinary cards.

The trick in this lecture Four Cards Name the Fifth Choose five cards. My assistant shows four. I name the fifth. Play the trick

Before this lecture

Ideas you will use

  • Card ranks/suits; modular counting

In this lecture

An outline of the lecture, scene by scene, with the statements that appear on screen. It follows the draft script, so details may change in production.

  1. Introduce the actual communication experiment

    At the table
    • Any five distinct cards
    • Partner chooses which to hide
    • Four identities + their order

  2. Partner encodes a genuine arbitrary hand

    At the table
    • Continuous preparation shot
    • No extra message
    • Read from decoder’s left

  3. Decode genuine row and reveal with an exact card-name branch

    At the table
    • Read row without moving it
    • Name one card before reveal
    • Fitch Cheney five-card trick

  4. Explain the same-suit anchor and short distance

    • J♣ +4 steps =2♣
    • Anchor first
    • Choose the direction of length 1–6

  5. Encode distance in the other three cards

    • Rank first; ties ♣<♦<♥<♠
    • LMH1 LHM2 MLH3 MHL4 HLM5 HML6
    • J♣ |8♦10♠2♥

  6. Explain guarantees and boundaries

    • Five→same suit
    • Choose short directed arc
    • Six orders→six offsets

  7. Specify partner trainer and a worked round

    • Assistant mode and decoder mode
    • Worked row→2♣
    • Four ordered names are sufficient

  8. Retrieve method and preview proofs

    • Choose target; orient pair; encode offset
    • Visible identities matter
    • Next: suit clock and permutation fluency

Companion interactive

Encode and decode any five-card hand.

The trick page is this lecture’s companion: be the spectator, lift the curtain to step through why it works, try the challenge, then learn the handling.

Open Four Cards Name the Fifth

Sources

How these sources were used
  • Colm Mulcahy, Mathematical Card Magic: Fitch Cheney mechanism. Course deliberately uses first-position anchor and rank-first suit-tie total order; book uses a different consistent convention.