The hardest problem on the hardest test

A difficult geometry puzzle with an elegant solution. Practice more problem-solving at Solution to the puzzle mentioned at the end: Special thanks to the following patrons: These videos exist thanks to Patreon: A different write-up of this solution: 1992 Putnam with this problem: A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! In the solutions for that problem, by the way, the that Calvin Lin is a friend of mine who works at Brilliant. Music by Vincent Rubinetti: