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Featuring James Grime. Bug Byte puzzle from Jane Street at https://bit.ly/janestreet-bugbyte and programs at https://bit.ly/janestreet-programs (episode sponsor) --- More links & stuff in full description below ↓↓↓ Dr James Grime discussing triangular numbers, cubes, pentagonal numbers, hexagonal numbers, tetrahedral numbers and Pollock's Conjecture. James Grime: https://www.singingbanana.com More James on Numberphile: http://bit.ly/grimevideos Sixty Symbols physics videos: / sixtysymbols Patreon: / numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We're also supported by the Simons Laufer Mathematical Sciences Institute (formerly MSRI): http://bit.ly/MSRINumberphile Our thanks also to the Simons Foundation: https://www.simonsfoundation.org NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: / numberphile Numberphile tweets: / numberphile Subscribe: http://bit.ly/Numberphile_Sub Video by Brady Haran and Pete McPartlan Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: / bradyharan Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Thanks to viewers for helping find the 343867 sums, including Arne, Alex, Sam, Felipe, Pablo, Ewoud and Michael.