Magic & Math with Cards

Lecture 50 · Performance

Last cards match

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 a checked opposite-order packet matching routine using fixed-total rotations and elimination.

The trick in this lecture Last Cards Match Choose which packet to rotate, eleven moves a round. Every discarded pair matches, and so do the last two cards. Play the trick

Before this lecture

Nothing. This lecture is a fine place to start.

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. Perform first elimination

    At the table
    • Move top→bottom in same packet
    • 11 moves total

  2. Repeat at smaller sizes

    At the table
    • Sizes 4→3→2→1

  3. Reveal the matching pairs

    At the table
    • Last ranks match

  4. Derive top-index relation

    • Match iff a+b ≡ m−1 (mod m)

  5. Track an exact sample

    • (3, 8); (5, 6); (4, 7)

  6. Prove preservation after removal

    • Matched removal restores reverse order

  7. Explain the fixed total

    • T+1 divisible by 4, 3, 2
    • lcm(4, 3, 2)=12

  8. Play and retrieve

    • Fixed total; free allocation

Companion interactive

Choose every rotation side and explain why matching survives each elimination.

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 Last Cards Match

Sources

How these sources were used
  • Numberphile, “Chinese Remainder Theorem and Cards (Tadashi Tokieda)”: Opposite-order last-card matching inspiration. Exact four-rank rotation/elimination version and count rule derived and checked; no sleight or COAT reversal.