Category Archives: Uncategorized

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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Picking a perfect NCAA bracket: 2018 was the most unlikely tournament so far

Introduction Every year, there are upsets and wild outcomes during the NCAA men’s basketball tournament. But this year felt, well, wilder. For example, for the first time in 136 games over the 34 years of the tournament’s current 64-team format, … Continue reading

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Whodunit logic puzzle

You are a detective investigating a robbery, with five suspects having made the following statements: Paul says, “Neither Steve nor Ted was in on it.” Quinn says, “Ray wasn’t in on it, but Paul was.” Ray says, “If Ted was … Continue reading

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Coupling from the past

Introduction This is a follow-up to one of last month’s posts that contained some images of randomly-generated “lozenge tilings.” The focus here is not on the tilings themselves, but on the perfectly random sampling technique due to Propp and Wilson … Continue reading

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How high can you count in limited space?

Introduction I recently saw several different checks, all from the same bank, each with a different dollar amount printed in a fixed-width font, similar to the shortened example below: **PAY EXACTLY**twelve thousand thirty-four and 56/100**************** Counting asterisks confirmed that the … Continue reading

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Proofs and theorems without words

Introduction In the figure below, a regular hexagon with side length 12 is tiled with “lozenges,” sort of like triangular dominoes, each consisting of a pair of unit-length equilateral triangles joined at a common side. Each lozenge is in one … Continue reading

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