The Nugget Algorithm
The Frobenius Number -- also called the McNugget Number -- is the highest number you can’t make out of two integers that have a greatest common divisor of 1. This late 19th-century math quirk was examined by Ferdinand Frobenius and expanded on by JJ Sylvester, but it came to public consciousness by examining the impossible orders of McDonald’s McNuggets in the United Kingdom. Poring over the possibilities of ordering chicken nuggets might seem like a trivial affair, but the concept of the Frobenius Number appears in important aspects of real life. It’s the beginning of thinking about optimization in certain areas, like the coin-based currencies we use worldwide. What denominations of coins are best mathematically? Which combinations fit best with how humans actually think and live? And that’s how we started thinking about whether the United States could need an 18-cent coin. By looking how we can combine nuggets and how we utilize coins -- including a “greedy algorithm” that helps us select the method in which we make change -- I found that sometimes the most optimal mathematical way of doing things just isn’t the right fit for how we navigate the world. ** LINKS ** How To Order 43 Chicken McNuggets by Numberphile • How to order 43 Chicken McNuggets (Frobeni... Chicken Nugget Numbers by DataGenetics http://datagenetics.com/blog/august22... Jeffrey Shallit https://cs.uwaterloo.ca/~shallit/pape... What This Country Needs is an 18 Cent Piece by Jeffrey Shallit https://cs.uwaterloo.ca/~shallit/Pape... Formula For the Frobenius Number In Three Variations http://web.iitd.ac.in/~atripath/publi... ** VSAUCE LINKS ** Vsauce2 Links Twitter: / vsaucetwo Facebook: / vsaucetwo Hosted and Produced by Kevin Lieber Instagram: / kevlieber Twitter: / kevinlieber Podcast: / thecreateunknown Research And Writing by Matthew Tabor / tabortcu Editing by Aspect Science / @tommocarroll Huge Thanks To Paula Lieber https://www.etsy.com/shop/Craftality Select Music By Jake Chudnow: / jakechudnow #education #vsauce2
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