Uploaded December 2024 | Updated September 2026, 2 weeks ago
Learn more about Jane Street’s internship opportunities: jane-st.co/SUM-internships
Sign up to patreon to get a unique christmas card! patreon.com/standupmaths
A Mathematical Secret Santa Protocol by Katie Steckles youtube.com/watch?v=ehRTbNIr6-E
This is the math stackexchange discussion: math.stackexchange.com/a/2896914
The Problems with Secret Santa, Hannah fry on Numberphile. youtube.com/watch?v=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 youtube.com/@samhartburn
2. Matt Parker youtube.com/@standupmaths
3. Matthew Scroggs youtube.com/@scroggs2
4. Brady Haran youtube.com/@numberphile
5. Geoff Marshall youtube.com/@geofftech2
6. Henry Reich youtube.com/@MinutePhysics
7. Mithuna Yoganathan youtube.com/@LookingGlassUniverse
8. Kat Phillips youtube.com/@KatDoesMaths
9. Steve Mould youtube.com/@SteveMould
10. Sophie Maclean youtube.com/@sophiemaclean9999
11. Peter Rowlett youtube.com/@peterrowlett
12. Katie Steckles youtube.com/@KatieSteckles
13. Grant Sanderson youtube.com/@3blue1brown
14. Tom Murphy VII youtube.com/@tom7
15. Destin Sandlin youtube.com/@smartereveryday
16. Ben Sparks youtube.com/@SparksMaths
17. Ayliean MacDonald youtube.com/@Ayliean
18. Rohin Francis youtube.com/@MedlifeCrisis
Huge thanks to my Patreon supporters. They're the real meaning of christmas. 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: standupmaths.com
Learn more about Jane Street’s internship opportunities: jane-st.co/SUM-internships
Sign up to patreon to get a unique christmas card! patreon.com/standupmaths
A Mathematical Secret Santa Protocol by Katie Steckles youtube.com/watch?v=ehRTbNIr6-E
This is the math stackexchange discussion: math.stackexchange.com/a/2896914
The Problems with Secret Santa, Hannah fry on Numberphile. youtube.com/watch?v=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 youtube.com/@samhartburn
2. Matt Parker youtube.com/@standupmaths
3. Matthew Scroggs youtube.com/@scroggs2
4. Brady Haran youtube.com/@numberphile
5. Geoff Marshall youtube.com/@geofftech2
6. Henry Reich youtube.com/@MinutePhysics
7. Mithuna Yoganathan youtube.com/@LookingGlassUniverse
8. Kat Phillips youtube.com/@KatDoesMaths
9. Steve Mould youtube.com/@SteveMould
10. Sophie Maclean youtube.com/@sophiemaclean9999
11. Peter Rowlett youtube.com/@peterrowlett
12. Katie Steckles youtube.com/@KatieSteckles
13. Grant Sanderson youtube.com/@3blue1brown
14. Tom Murphy VII youtube.com/@tom7
15. Destin Sandlin youtube.com/@smartereveryday
16. Ben Sparks youtube.com/@SparksMaths
17. Ayliean MacDonald youtube.com/@Ayliean
18. Rohin Francis youtube.com/@MedlifeCrisis
Huge thanks to my Patreon supporters. They're the real meaning of christmas. 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: standupmaths.com
