Magic & Math with Cards

Lecture 60 · Performance

The 124-card finale

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 the explicit 124-card communication protocol and connect its arithmetic to optimality and existence proofs.

The trick in this lecture The 124-Card Finale Five cards drawn from a deck of 124. Four shown, the fifth named. Play the trick

Before this lecture

Ideas you will use

  • Rehearsed two-person protocol

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 numbered-deck finale and exact choices

    At the table
    • 124 distinct numbered cards
    • Spectator chooses five; assistant chooses hidden card
    • Only ordered visible labels are transmitted

  2. Assistant executes exact general encoder

    At the table
    • Sort→select hidden→candidate index→permutation
    • Worksheet is preparation evidence
    • Decoder sees only final ordered row

  3. Decoder computes and commits to exact number branch

    At the table
    • Record order before sorting
    • Compute independently
    • Commit before uncovering

  4. Explain worked hand selection and candidate position

    • Hide 87
    • Compressed 84 is candidate 17
    • Send 59,93,23,27

  5. Work inverse decoding and boundary example

    • Permutation 17→compressed 84→original 87
    • Boundary row 1,2,3,4→hidden 5
    • Update candidate after every restored gap

  6. Compare existence proof and explicit performance

    • Upper bound
    • Existence under compatibility
    • Explicit computation

  7. Specify complete finale companion and learner challenge

    • Two-person mode
    • Guided and unassisted decoding
    • Independent encode/decode comparison

  8. Close course through in variants and information

    • Allowed actions
    • Surviving or encoded information
    • A shared experiment

Companion interactive

Play the complete two-person 124-card protocol on arbitrary five-label hands.

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 The 124-Card Finale

Sources

How these sources were used
  • Norman Do, “A Mathemagical Card Trick”: Exact Do convention used consistently in performance and worked examples.
  • Shai Simonson and Tara S. Holm, “Using a Card Trick to Teach Discrete Mathematics”: Related constructive scheme has shifted hidden-position convention; do not mix conventions.