This essay starts with a puzzle I posed on twitter, which led to a next puzzle, and a next. My thanks to  @republicofmath and @sted304A for computing very very triangular numbers, and to @daveinstpaul for an elegant idea giving a proof.    OPENING PUZZLER:   The sequence of numbers that are the sum of two […]

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OPENING PUZZLER  Stack \(n\) coins at the origin on the number line and let them spread across it according to the following rule: Identify a stack with two or more coins on it and then “fire” that stack.  That is, move two coins off the identified stack and set one coin one unit to the […]

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