Category Archives: Uncategorized

Disabling subnormals in MATLAB

Suppose that we want to compute the following expression, somewhat contrived in complexity for the purpose of example: The following MATLAB code implements this formula, and measures the time required to evaluate it: Now suppose that we execute this same … Continue reading

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A lattice path puzzle

This past week’s Riddler puzzle on FiveThirtyEight asks for the number of different paths of minimum length from a starting intersection of city streets to a destination blocks east and blocks north. Put another way, moving on the 2D integer … Continue reading

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Arbitrary-precision rational arithmetic in C++

Introduction This is a follow-up to a post from several years ago describing a C++ implementation of arbitrary-precision unsigned integer arithmetic. This weekend I extended this to also support arbitrary-precision signed integers and rational numbers. Although this started as an educational … Continue reading

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Uncertainty in trading passengers for fuel

I had an interesting experience recently while preparing for a flight from Los Angeles to Baltimore. It was a completely full flight– initially, at least– with myself and 174 other passengers who had already boarded the Southwest 737-800, seemingly ready … Continue reading

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An urn puzzle

It has been a while again since I last posted a puzzle, so… You have once again been captured by mathematically-inclined pirates and threatened with walking the plank, unless you can win the following game: some number of black balls … Continue reading

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On average, we die a decade earlier than expected

“Doctors say he’s got a 50/50 chance of living… though there’s only a 10% chance of that.” I’ve lately had occasion to contemplate my own mortality. How long should I expect to live? The most recent life table published by the Centers … Continue reading

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How many melodies are there?

Introduction The title question came up recently, which I think makes for an interesting combinatorics exercise. The idea is that, given the extent of “borrowing” of past musical ideas by later artists, are we in danger of running out of … Continue reading

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