A Lifelong Mathematical Obsession

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⬡ PATREON:   / anotherroof  
⬡ CHANNEL:    / anotherroof  
⬡ WEBSITE: https://anotherroof.top
⬡ SUBREDDIT:   / anotherroof  

Contact me via my personal website if you’d like to hire me as a tutor:
⬡ https://www.drmcgaw.co.uk

⬣ ABOUT ⬣
All my life, I have been obsessed with a counting puzzle I came up with as a child. Turns out, I’m not the first to think about it. Known as Hertzsprung’s Problem or the n-kings problem, I present an elementary proof of the general formula given by Morton Abramson and William Moser.

⬣ TIMESTAMPS ⬣
00:00:00 - Introduction and History
00:11:04 - Overview
00:17:14 - Stars & Bars
00:23:44 - Inclusion-Exclusion Principle
00:29:31 - Pascal’s Triangle
00:33:27 - Forbidden Pair Options Part 1
00:43:51 - Forbidden Pair Options Part 2
00:51:55 - Number of Permutations
00:55:52 - Putting it all Together
01:03:22 - A Cleaner Way?
01:06:40 - Outro

⬣ INVESTIGATORS ⬣
Nothing for you in this one. Sorry!

⬣ REFERENCES ⬣
M Abramson and W Moser, Combinations, Successions and the n-Kings Problem. Mathematics Magazine, Vol. 39, No. 5 (Nov., 1966), pp. 269-273.

⬣ CREDITS ⬣
Music by Danjel Zambo.

Images
Explosion:
https://www.vecteezy.com/video/297431...
Hertzsprung-Russell Diagram, European Southern Observatory:
https://commons.wikimedia.org/wiki/Fi...
Ejnar Hertzsprung and Severin Hertzsprung are public domain.