Communicating the Card

An implementation of the algorithm described in part 5 of the paper Using a Card Trick to Teach Discrete Mathematics by Shai Simonson and Tara S. Holm.
I first heard about this trick in December 2017 from hpmetsfan.
I performed this trick for the 24 Hour Maths Magic Show, which you can see on Youtube
On my first day of teaching MATH 106: Combinatorics at Harvey Mudd College in Spring 2024, I performed a version of this trick called "Fitch Cheney's Five Card Trick" with Art Benjamin, who was responsible for rediscovering and popularizing the trick.

Assistant Instructions

Have the magician leave the room, and ask audience for five distinct numbers between 1 and 100, inclusive.
Type these numbers below, comma separated. (e.g. 27, 87, 93, 23, 59)
{"controller"=>"card_trick", "action"=>"index"}
Audience numbers:
[?, ?, ?, ?] ← (Once you hit "Compute!", four of the numbers should appear here.)
Read the four numbers to the magician in the order that they appear.