Author Archives: possiblywrong

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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Hilbert halftone art

Introduction This post was motivated by a recent attempt to transform a photograph into a large digital print, in what I hoped would be a mathematically interesting way. The idea was pretty simple: convert the (originally color) image into a … Continue reading

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Probability of playable racks in Scrabble

Introduction Earlier this year, I spent some time calculating the probability of a Scrabble “bingo:” drawing a rack of 7 tiles and playing all of them in a single turn to spell a 7-letter word. The interesting part of the … Continue reading

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