Can You Solve The Diagonal Counting Puzzle?

Thanks to Patrick from Germany for suggesting this problem! Students were supposed to solve it in less than 1 minute with no calculator. Special thanks this month to: Nida Davis, Richard Ohnemus, Shrihari Puranik, Kyle, Michael Anvari . Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions

References
2018 Raytheon MATHCOUNTS National Competition (link includes timestamp around 35:34)

Math StackExchange
https://math.stackexchange.com/questions/3541143/2018-mathcounts-let-dk-be-the-number-of-diagonals-for-a-polygon-with-k-si

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