Magic & Math with Cards

Lecture 29 · Mathematics

Why reversing one packet matters

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What you will learn

Prove why reversal yields mixed aligned pairs.

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. Why reverse one packet?

    • Cut-only counterexample: 1, 5

  2. What stays consecutive?

    • Prefix set={3, 4, 5, 6}
    • Next: 2 or 7

  3. Why does every pair work?

    • b−a+1 even
    • (b+1)−(a−1) odd

  4. Does source determine colour?

    • AA | BB | AB | BB
    • Source ≠ colour

  5. Which pairs are promised?

    • Aligned pairs ≠ sliding windows

  6. What are the hypotheses?

    • Alternation
    • Reversal
    • Order
    • Alignment

  7. Can you break the stronger claim?

    • Example checks ≠ proof

  8. What has been proved?

    • Prefixes are intervals
    • All aligned pairs mixed

Companion interactive

Planned

Find which missing hypothesis permits a bad pair.

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: Two-frontier and interval explanation.
  • Colm Mulcahy, Mathematical Card Magic: Alignment and reverse-deal conditions.