Magic & Math with Cards

Lecture 20 · Mathematics

More than two colours

Suits as an alphabet

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What you will learn

Generalize window codes to larger alphabets while checking capacity, cyclic uniqueness and physical card supply.

Before this lecture

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. Compare information from colour and suit

    • 2 colours; 4 suits
    • Two colour reports: 2²=4
    • Two suit reports: 4²=16

  2. Define general alphabet and capacity

    • q symbols, k length →qᵏ words
    • Full cycle length=qᵏ
    • Capacity does not construct a stack

  3. Construct and verify suit-pair cycle

    • 0=C,1=H,2=S,3=D
    • 0010203112132233
    • SD=23 identifies one window

  4. Generalize graph construction to q symbols

    • 4 vertices; 16 directed edges
    • Each vertex: 4 in,4 out
    • Same Euler proof, different alphabet

  5. Account for physical card supply

    • 16-cycle: 4 cards per suit
    • 64-cycle: 16 per suit >13 available
    • Specify which identities must be distinguished

  6. Compare decoding effort and information budgets

    • 4 binary reports ↔2 suit reports
    • Same 16 addresses, different questions
    • Location layer +identity layer

  7. Companion construction and sample decoding

    • Goal: all 16 ordered pairs
    • SD →4S,3D
    • Check windows and card supply separately

  8. Synthesize limits without overclaiming 52 stack

    • Alphabet ×window determines capacity
    • Construction must meet physical constraints
    • Next: relative order as an observation

Companion interactive

Planned

Build a 16-position suit cycle with all ordered pairs and decode exact card names.

The interactive for this lecture is being built and will appear here.

Notes

Written notes for this lecture will appear here.

Sources

How these sources were used
  • Persi Diaconis and Ron Graham, Magical Mathematics: Larger-alphabet and product effects motivate the topic; explicit 16 suit cycle is a checked teaching construction.