Magic & Math with Cards

Lecture 06 · Performance

Ten cards, always five face up

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 the ten-card face-up prediction and explain why equal odd/even face-up counts force a five-and-five finish.

The trick in this lecture Always Five Face Up Ten cards, cut and turned however you like. Turn over every second card, and exactly five end up face up. Play the trick

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. Set an exact numerical prediction and demonstrate mixing

    At the table
    • 10 cards, all down
    • Cut any amount
    • Turn top TWO TOGETHER
    • Stop when you choose

  2. Execute visible unambiguous finish and count result

    At the table
    • Flip positions 2, 4, 6, 8, 10
    • Flip current face; do not set it UP
    • Exactly 5 up and 5 down

  3. Repeat and introduce the hidden two-lane count

    At the table
    • Odd lane: 1, 3, 5, 7, 9
    • Even lane: 2, 4, 6, 8, 10
    • Before finish: equal face-up counts

  4. Count the finish from a balanced intermediate state

    • Before: odd=a, even=a
    • After: odd=a, even=5−a
    • a+(5−a)=5

  5. Prove cuts preserve equality for ten cards

    • Cut 1 exchanges the lanes
    • Equal counts remain equal
    • Any cut = repeated Cut 1

  6. Prove top-pair turnover preserves equality

    • DD: add 1 to each lane
    • UU: remove 1 from each lane
    • DU or UD: no count change
    • Balance survives every legal step

  7. Audit exact run and demonstrate missing hypothesis

    • Sample before: up at 1, 4, 5, 10
    • Sample after: up at 1, 2, 5, 6, 8
    • Bad start: one up → six up after finish

  8. Specify count-prediction game and retrieval

    • Predict 5 before finish
    • Explain: 2+3=5
    • Change one rule; locate the failed step

Companion interactive

Predict exactly five up after legal mixing and correct alternating flip; diagnose altered rules.

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 Always Five Face Up

Sources

How these sources were used
  • Persi Diaconis and Ron Graham, Magical Mathematics: Hummer ten-card effect and balance proof; row finish is an explicit teaching handling of flipping every second card.
  • Colm Mulcahy, Mathematical Card Magic: Equal face-up counts at odd/even positions after CATO from all-alike orientation.