Two Combinatorial Identities in Minecraft @DrWeselcouch

Uploaded March 2021 | Updated September 2026, 4 hours ago

In this video we show that 1+3+5+...(2n-1) = n^2. We use this along with a fact proven in a previous episode to show that the sum of the first n cubes is n+1 choose 2 squared.

Where we've used the redstone machine before:
youtu.be/6KdxCPGEtbE
youtu.be/60Yd-apGun0

Sum of the first n+1 choose 2 odd numbers equals the sum of the first n cubes:
youtu.be/PDOU8SUhrrk

You can see all of my previous Math and Minecraft episodes here:
youtube.com/playlist?list=PLscpLh9rN1Rf-dqLO4r3GAwvm1O_xL7D1

Make sure to subscribe for more Math and Minecraft episodes. Please share this video with any Minecraft and Math lover in your life :)
youtube.com/c/drweselcouch

#Combinatorics #Minecraft #FunMath #Education

Two Combinatorial Identities in Minecraft

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$A beautiful combinatorics problem! In this video we count the number of subsets of {1, 2, ..., 2n+1} that have no two elements that differ by 2. The same questions, but subsets of {1, 2, ..., 2n} https://youtu.be/jEAMCTh9-xA Subscribe and Ring the 🔔 https://www.youtube.com/c/DrWeselcouch Discord 🎮 https://discord.gg/7JUbZ2cVXr Reddit 👽 https://www.reddit.com/user/CoffeeAndCalcWithDrW PLAYLISTS 🎵 : Number Theory Problems: https://youtube.com/playlist?list=PLscpLh9rN1RfOeiBA6o4YSXtAWF3-3_AT Multivariable Calculus Problems: https://youtube.com/playlist?list=PLscpLh9rN1RcdbQLLvRItUxOMRKnbDJaw Calculus 2 Problems: https://youtube.com/playlist?list=PLscpLh9rN1RcqIZyidbChYLuMAdZhhEwN Math and Minecraft: https://youtube.com/playlist?list=PLscpLh9rN1Rf-dqLO4r3GAwvm1O_xL7D1 Combinatorics Problems: https://youtube.com/playlist?list=PLscpLh9rN1RfNzyUsA_KzsfQ_k1AR9Ebs Geometry Problems: https://youtube.com/playlist?list=PLscpLh9rN1RdFKjA3-vvTL_xG6s3YxB6r Calculus Problems: https://youtube.com/playlist?list=PLscpLh9rN1Rcv3XYXq5Z0oXMEOVL-aocI Linear Algebra Problems: https://youtube.com/playlist?list=PLscpLh9rN1Rfo0ifw9RZFoJ2Te2jk_pwX Statistics Problems: https://youtube.com/playlist?list=PLscpLh9rN1RexwCjV9_1RmfluCTv5HKe1$

When in doubt, INTEGRATE! (ft. Blackpenredpen)

Calculators are for the weak! Use Algebra instead!