Puzzles with beautiful solutions - Binary, Hanoi and Sierpinski, part 1

Binary counting can solve the towers of Hanoi puzzle, and if this isn't surprising enough, it can lead to a method for finding a curve that fills Sierpinski's triangle (which I get to in part 2). Thanks to Desmos for their help in supporting this video. They're hiring, and anyone interested should check out https://www.desmos.com/careers Thanks to all Patreon supporters as well, you can support and get early access to future "Essence of" series here: https://www.patreon.com/3blue1brown I also want to give a special shoutout to the following patrons: CrypticSwarm, Ali Yahya, Dave Nicponski, Juan Batiz-Benet, Yu Jun, Othman Alikhan, Markus Persson, Joseph John Cox, Luc Ritchie, Einar Wikheim Johansen, Rish Kundalia, Achille Brighton, Kirk Werklund, Ripta Pasay, Felipe Diniz, Chris, Curtis Mitchell, Ari Royce, Bright , Myles Buckley, Robert P Zuckett, Andy Petsch, Otavio good, Karthik T, Steve Muench, Viesulas Sliupas, Steffen Persch, Brendan Shah, Andrew Mcnab, Matt Parlmer, Naoki Orai, Dan Davison, Jose Oscar Mur-Miranda, Aidan Boneham, Brent Kennedy, Henry Reich, Sean Bibby, Paul Constantine, Justin Clark, Mohannad Elhamod, Denis, Ben Granger, Jeffrey Herman, Jacob Young.