Where Discovery Begins

# The hardest problem on the hardest test

A difficult Putnam question with an elegant solution.
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Special thanks to these supporters: http://3b1b.co/putnam-thanks

Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/

These videos exist thanks to Patreon:
https://www.patreon.com/3blue1brown

A different write-up of this solution:
http://lsusmath.rickmabry.org/psisson/putnam/putnam-web.htm

1992 Putnam with this problem:
http://kskedlaya.org/putnam-archive/1992.pdf

A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! The solution for that problem, by the way, was written by Calvin Lin, a friend of mine who works at Brilliant. Small world!
http://kskedlaya.org/putnam-archive/2005.pdf
http://kskedlaya.org/putnam-archive/2005s.pdf

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Animations largely made using manim, a scrappy open source python library. https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it’s not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then “add subtitles/cc”. I really appreciate those who do this, as it helps make the lessons accessible to more people.
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