Pascal's Busted Valve
A plumber diagnoses a 'busted valve' in Pascal's triangle and estimates how the error propagates to later rows.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-06-26-pascal-s-busted-valve/ (CC BY-NC 4.0)Transcript
[Pascal's triangle with an error: row 5 shows 6 where 10 should be, and the error propagates below (16, 11, 31, 27, 17…)]
[1] Plumber: "I found your problem, Mr. Pascal. There's a busted valve where ₙCₖ feeds into ₙ₊₁Cₖ." Pascal: "Ugh. What's it going to cost me?"
[2] Plumber: "By row R? Well, ballpark, I'd say something like 2^(R−n−1) ₙCₖ." Pascal: "UGHHHHH"