A difficult Putnam question with an elegant solution.
This video was sponsored by Brilliant: https://brilliant.org/3b1b
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/putnam-thanks
Home page: https://www.3blue1brown.com/

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

These videos exist thanks to Patreon:
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A different write-up of this solution:
http://lsusmath.rickmabry.org/....psisson/putnam/putna

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.
Download the music on Bandcamp:
https://vincerubinetti.bandcam....p.com/album/the-musi

Stream the music on Spotify:
https://open.spotify.com/album..../1dVyjwS8FBqXhRunaG5

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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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

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Our English and Maths courses at Friends Centre. Find out more about our English and Maths classes, get testimonials from our learners and see what we do in class when you study with us!

Route leader and students discuss their highlights of our (Secondary) Mathematics PGCE and why you should train to teach at the University of Brighton.

Curious about this course?
Find out more:
http://www.brighton.ac.uk/cour....ses/study/secondary-

Melo Bradford and Richard Harvey-Swanston chat about our specialist primary mathematics teacher training course.

Curious about becoming a becoming a primary teacher? Find out more: https://www.brighton.ac.uk/stu....dying-here/subject-a

Read insights from a student on the course:

https://blogs.brighton.ac.uk/s....tudentbloggers/2023/

Hør vores produktionschef Rene Bank fortælle om, hvad forberedelsespakker går ud på og hvorfor de er vigtige.

Gennemgang af poesi: digtning på vers. Herunder: Jambe, elegi, epigram og melisk poesi.

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Se hele videoen på www.restudy.dk

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Denne video handler om, hvornår man skal bruge bestemt og ubestemt.

Majbritt havde, som så mange andre forældre, svært ved at hjælpe hendes datter med lektierne. Det valgte hun at gøre noget ved! Står du i samme situation?

Subscribe to the Official Monty Python Channel here - http://smarturl.it/SubscribeToPython
Galaxy Song, taken from Monty Python's The Meaning of Life. Terry Jones picked this as part of his Top 10 Monty Python Movie Moments for Esquire Magazine -
"It's such a lovely song. I think it's one of the best things Eric [Idle]'s ever done. There was going to be more animation but Terry was so busy with other parts of the film we ended up using more of the live-action parts that I'd shot for safety."
See the full list here - -http://www.montypython.com/news_terryjtop10/160

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Visit the NEW Monty Python iTunes store - http://smarturl.it/MontyPython1D5TGitun

Welcome to the official Monty Python YouTube channel. This is the place to find top quality classic Python videos, as well as some special stuff that you'll only find here such as interviews and behind-the-scenes footage from our live shows. All the Pythons including John Cleese, Michael Palin, Eric Idle, Terry Gilliam, Terry Jones & Graham Chapman can be found here being incredibly silly.

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DOWNLOAD / DVD / LICENSE @ https://www.naturerelaxation.c....om/products/splendor | WATCH ON DEMAND (no Ads or Watermarks) @ https://watch.naturerelaxation.....com/videos/splendor | SPLENDOR: (noun) brilliant or gorgeous appearance; grandeur. | ABOUT THE FILM: The latest - and greatest yet- of our extended length ambient films, "Splendors of Nature" sweeps viewers on an all-day-long, breathtakingly beautiful & immersive audiovisual journey that dives deep into very heart of Nature. Featuring countless displays of grandeur from the around the world, this 12 hour long film offers a seamless relaxation experience that gently flows from one wonder to the next. From snowy mountain forests to swimming with colorful coral reef sea life; from the plains of Africa to the distant fjordlands of Iceland, this Nature Relaxation film truly has something for everyone - even space lovers! MORE INFO / CREDITS:

SPLENDORS OF NATURE is a compilation of multiple existing films from our collection, including:
Snowy Mountain Dreamland
Birds of the Rainforest
Flying Over Oahu
Redwood Forest Rejuvenation
Amazing Africa (The Animals Video was filmed by Robert Hofmeyr, ProArtInc, for more Animal videos please visit https://www.youtube.com/watch?v=3xPkwNu2o8g&t=12404s )
Flying Over Italy
Rainbow Reef Relaxation
Dolphin Voyage Relaxation
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America's Beautiful West
Turtle Paradise
Above the Dolomites
Beyond Infinity

Coming Shortly to Nature Relaxation On-Demand. Try free for 30 days @ https://www.NatureRelaxation.com/Try

CREDITS: Featuring Cinematography by David Huting, Nick Skeyes, Noel Thomas, Peter Schneider, Tilo & Yvonne Kuhnast, Roman Khomylak, and Nimanty; learn more about the team of creators behind NRF @ https://www.NatureRelaxation.com/Team

MUSIC: By Relax Moods @ https://www.RelaxMoods.com (Also featuring Barry Kernachan, & Dominic Stone)

NASA's Kepler mission has confirmed the first near-Earth-size planet in the “habitable zone” around a sun-like star. This discovery and the introduction of 11 other new small habitable zone candidate planets mark another milestone in the journey to finding another “Earth.”

The newly discovered Kepler-452b is the smallest planet to date discovered orbiting in the habitable zone -- the area around a star where liquid water could pool on the surface of an orbiting planet -- of a G2-type star, like our sun. The confirmation of Kepler-452b brings the total number of confirmed planets to 1,030.

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They better put some respect on our kids names! Act like ya know! #homeschoolpride

This is a “concern” that friends and family would bring up often when I told them I was homeschooling my children, before the pandemic. I’m really not sure where people get this idea from that school is the only place, or even the best place to socialize a child.

In short, our children are not only fine but thrive when it comes to interacting nicely with others.

Now some hard truth:

As a teacher, many of the schools I’ve taught in or visited are the last place I would want my child to be socialized. That even includes so called good schools in a blue rated school districts where Socialization looks like:

- Girls being teased for plump or skinny bodies, developing body image and confidence issues
- Sexual harassment and touching as early as kindergarten
- Dehumanization and degradation of children by adults
- Physical restraint and choking by adults
- Dark skinned boys being treated unfairly and undervalued by adults and children

So when people complain that my children won’t be socialized, it takes a lot for me not to roll my eyes. But I understand, this is the only type of socialization we in America, where all children have access to go to school, understand.


#homeschool #homeschoolmom #homeschooling #blackhomeschoolers #melanin #blackkids #blackmoms #teachermom

Climate change is already increasing extreme weather events and impacting communities and schools across the country. To continue supporting students in a changing climate, schools must adapt and build resilience.

K12 Climate Action is on a mission to unlock the power of the education sector to be a force for climate action, solutions, and environmental justice. Learn more about K12 Climate Action at K12ClimateAction.org.

Video Transcript:

Climate change is increasing extreme weather events. Families and schools around the country are already being affected. This trauma, this disruption, this uncertainty is happening now. Schools can adapt, build resilience, and prepare for what’s coming. Schools can also teach about climate resilience and prepare youth to live in a changing climate. We must meet this moment to protect our future. Mitigate, adapt, advance equity, educate. This is Planet Ed. K-12 Climate Action. The Aspen Institute. Share if you want schools to adapt and build resilience for climate change. K12ClimateAction.org #k12ClimateAction

The solar system's most distant planet, Neptune, is a colossal world that still baffles scientists even today. Only one robotic spacecraft, called Voyager 2, has ever visited the planet, briefly allowing us to study its complex, dramatic atmosphere like never before. This is the only close-up footage ever captured of Neptune and reveals what it would be like to approach the ice giant planet towards the edge of the solar system.

Footage credit: NASA

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WOOHOO! Learn the planets of our solar system in this video for kids of all ages! You will discover what a planet is, what the two types of planets are and the two different kinds of primary planets! Plus, you will learn some exciting facts about each of the primary planets! Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune will all be familiar friends after this video!


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Thanks for learning with us today! We hope to see you next video!

Homeschool Pop Team

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