Magic & Math with Cards

Section 6 of 7

Assorted Tricks

Base three, Fibonacci numbers and clock arithmetic, each hiding in a deal.

Three tricks and three different pieces of mathematics: writing a number in base three, sums of Fibonacci numbers, and remainders on clocks of different sizes.

Lectures
46–51
Running time
About two hours
Formats
Three performances, three mathematics lectures

Performance lecture, with a trick to play Mathematics lecture

  1. The 27-card trick: choose the destination

    Name a number from 1 to 27 and think of a card. After three deals, your card is at exactly that number.     Play The 27-Card Trick

  2. A card position written in base three

    Derive the ternary target code, prove convergence after three adaptive rounds, and distinguish the 21-card version.

  3. Little Fibs: two cards from their sum

    Choose two of six cards and tell me only their total. I'll name both.     Play Little Fibs

  4. Unique sums—and where they stop being unique

    Prove distinct-pair uniqueness for Fibonacci-style values, expose triple ambiguity, and decode four-card complements.

  5. Last cards match

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

  6. Remainders, common multiples and matching cards

    Derive fixed-total matching from rotations and explain common multiples, coprime CRT and compatible noncoprime clocks.