2024-12-23

[public] 164K views, 11.0K likes, dislikes audio only

Stand-up Maths

Learn more about Jane Street’s internship opportunities: https://jane-st.co/SUM-internships

Sign up to patreon to get a unique christmas card! https://www.patreon.com/standupmaths

A Mathematical Secret Santa Protocol by Katie Steckles https://www.youtube.com/watch?v=ehRTbNIr6-E

This is the math stackexchange discussion: https://math.stackexchange.com/a/2896914

The Problems with Secret Santa, Hannah fry on Numberphile. /youtube/video/5kC5k5QBqcc

Thanks to everyone who took part! Here they are in the same random order as the emails went around. Not everyone is active on youtube so you may need to google some people. Or there's a 40% chance they're in a Numberphile video somewhere.

1. Sam Hartburn https://www.youtube.com/@samhartburn

2. Matt Parker https://www.youtube.com/@standupmaths

3. Matthew Scroggs https://www.youtube.com/@scroggs2

4. Brady Haran https://www.youtube.com/@numberphile

5. Geoff Marshall https://www.youtube.com/@geofftech2

6. Henry Reich https://www.youtube.com/@MinutePhysics

7. Mithuna Yoganathan https://www.youtube.com/@LookingGlassUniverse

8. Kat Phillips https://www.youtube.com/@KatDoesMaths

9. Steve Mould https://www.youtube.com/@SteveMould

10. Sophie Maclean https://www.youtube.com/@sophiemaclean9999

11. Peter Rowlett https://www.youtube.com/@peterrowlett

12. Katie Steckles https://www.youtube.com/@KatieSteckles

13. Grant Sanderson https://www.youtube.com/@3blue1brown

14. Tom Murphy VII https://www.youtube.com/@tom7

15. Destin Sandlin https://www.youtube.com/@smartereveryday

16. Ben Sparks https://www.youtube.com/@SparksMaths

17. Ayliean MacDonald https://www.youtube.com/@Ayliean

18. Rohin Francis https://www.youtube.com/@MedlifeCrisis

Huge thanks to my Patreon supporters. They're the real meaning of christmas. https://www.patreon.com/standupmaths

CORRECTIONS

- None yet, let me know if you spot anything other than protocol improvement.

--- Ok, here is what he think is the current best protocol. We'll give it a try next year! ---

For people P1 to Pn.

Goals of the system:

- no central authority needed

- can be done remotely with no hidden information

- does not give anyone their own name

- no one malicious actor can do anything to exploit the system without risk of breaking everything

Be as random as possible. No new random number can match any already on the list.

STAGE 0: POPULATE THE LIST

Everyone adds a pair of random numbers, shuffles the list, and passes it on.

STAGE 1: DO THE SHUNT

P1 shuffles the list and then shunts the pairs along one space to form new pairs (last number wraps to first number).

Everyone from P2 to Pn-1 uses a 50% probability of also shunting an extra space in the same direction. Pn definitely does not shunt.

No one shuffles. Everyone replaces their random numbers.

STAGE 2: THE CHECK

Everyone looks to see where their numbers are and remembers their exact location. If they move at any point from now on, a player should raise the alarm that the system has been compromised.

No one shuffles. Everyone replaces their random numbers.

STAGE 3: THE BIG REVEAL

Everyone replaces their 'left numbers' (aka 'receiver IDs') with their name of any other agreed system for identifying people. The other number is replaced with a new random number, no one shuffles.

STAGE 4: THE READ OUT

Goes around the loop again with everyone looking to see whose name their random number is paired with. This is who they buy a gift for. They then cover their tracks by swapping out the random number for a new one.

--- And for completeness, here is the protocol exactly as we tried it in this video. ---

STAGE 0: POPULATE THE LIST

Everyone adds a pair of random numbers, shuffles the list, and passes it on.

STAGE 1: DO THE SHUNT

P1 shuffles the list and then shunts the pairs along one space to form new pairs (last number wraps to first number).

STAGE 2: SWAP THE LIST

Everyone replaces their first random number with their name and their second random number with a new random number.

STAGE 3: THE BIG REVEAL

Goes around the loop again with everyone looking to see whose name their random number is paired with. This is who they buy a gift for. They then cover their tracks by swapping out the random number for a new one.

Filming and editing by Alex Genn-Bash

Written and performed by Matt Parker

Produced by Nicole Jacobus

Music by Howard Carter

Design by Simon Wright and Adam Robinson

Messing around by Everyone Else

MATT PARKER: Stand-up Mathematician

Website: http://standupmaths.com/