Magic & Math with Cards

Lecture 54 · Mathematics

Six messages in three cards

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What you will learn

Encode and decode all six triple permutations with explicit total-order conventions.

Before this lecture

In this lecture

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  1. Separate a permutation count from a working code

    • Reference order + permutation table + direction
    • Rank first; suits break ties
    • L, M, H belong to this triple

  2. Prove six orders and list all without omission

    • 3×2×1=6
    • 1 LMH; 2 LHM; 3 MLH
    • 4 MHL; 5 HLM; 6 HML

  3. Apply rank-first order and suit tie-break

    • 2♣<2♦<Q♠
    • 2♦, Q♠,2♣→MHL→4
    • A♦, A♠, A♥→LHM→2

  4. Give encoding and decoding as inverse procedures

    • Encode: sort→pattern→place
    • Decode: rank displayed cards→pattern→number
    • Five→J♠,3♥,7♣

  5. Expose disagreement in reference order

    • Same row, different convention
    • Rank-first: MHL→4
    • Suit-first: LMH→1

  6. Integrate offset with anchor without crossing roles

    • Anchor supplies suit and starting rank
    • Permutation supplies offset
    • No rank sum in fixed-anchor decoding

  7. Specify permutation trainer and error feedback

    • Six cases per triple
    • Accuracy before speed
    • Separate role errors from table errors

  8. Retrieve exact conventions and preview variable anchor

    • Roles travel with identities
    • Sorting a message erases its order
    • Next: compute the anchor position

Companion interactive

Planned

Send and read numbers 1–6 using any distinct triple.

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
  • Colm Mulcahy, Mathematical Card Magic: Six-permutation protocol; our rank-first convention is an explicitly stated adaptation of the book’s total order.