Magic & Math with Cards

Lecture 13 · Performance

Five colours reveal five cards

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

Decode five consecutive cards from the unique five-bit colour address of a prepared cyclic 32-card packet.

The trick in this lecture Five Colours, Five Cards Tell me only the colours of five cards. I'll name all five. Play the trick

Before this lecture

Ideas you will use

  • Card colours and straight cuts
  • Reading a fixed left-to-right order

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. Establish fair choices and fixed reading order

    At the table
    • Cut: top block to bottom
    • Places 1–5 remain fixed

  2. Select five consecutive cards and acquire colour word

    At the table
    • Only colour is reported
    • Read 1→2→3→4→5

  3. Reveal according to actual word then identify the mathematical question

    At the table
    • Prepared packet
    • Free cuts; no arbitrary shuffle

  4. Explain observations as an address

    • Black=0; red=1
    • 01001 → AS,2D,5C,3S,6D
    • One address identifies the whole window

  5. Count words and verify uniqueness

    • 2⁵=32 possible words
    • Count first; check collisions second
    • de Bruijn sequence

  6. Prove cuts preserve cyclic windows and distinguish illegal shuffle

    • A cut changes the origin
    • The cyclic neighbour relation remains
    • Consecutive + ordered observations

  7. Teach complete lookup performance and error awareness

    • 11111 →7H,6H,4H,8H, AD
    • Every word is valid: no automatic error detection
    • Rehearse accuracy before speed

  8. Companion challenge and retrieval

    • Goal: locate the window
    • Legal controls: cut, report, decode
    • Challenge: remove every collision

Companion interactive

Locate every cyclic five-card window from its colour report.

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 Five Colours, Five Cards

Sources

How these sources were used
  • Persi Diaconis and Ron Graham, Magical Mathematics: Prepared 32-card sequence and lookup; original presentation adapted to numbered mats for unambiguous order.