Category Archives: Uncategorized

Counting edge-matching puzzles

I recently re-discovered a puzzle that I had mostly forgotten from when I was a kid. The problem is simple to state: rearrange and rotate the seven hexagonal pieces shown below so that each of the twelve pairs of facing … Continue reading

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The Fisher-Yates shuffle is backward

Given a list of elements, such as cards in a deck, what is the right way to shuffle the list? That is, what is the appropriate algorithm to (pseudo)randomly permute the elements in the list, so that each of the … Continue reading

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Among Us: Morse code puzzle

In the online game Among Us, players who visit the Comms room hear a fuzzy audio recording of a series of high-pitched beeps that sound like Morse code. I first heard the recording here, but this more recent video also … Continue reading

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Counting Hotel Key Cards

Introduction Suppose that you are the owner of a new hotel chain, and that you want to implement a mechanical key card locking system on all of the hotel room doors. Each key card will have a unique pattern of … Continue reading

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Exploiting advantage from too few shuffles

Introduction A few days ago a friend of mine referred me to an interesting podcast discussing card shuffling, framed as a friendly argument-turned-wager between a couple about how many times you should shuffle a deck of cards. A woman claims … Continue reading

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Giant Yahtzee

In the game of Yahtzee, players roll five standard dice, then repeatedly re-roll subsets of the dice, trying to obtain various scoring combinations, the most valuable of which is a “Yahtzee,” or five of a kind, i.e., all five dice … Continue reading

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MATLAB’s colon operator and for loops

Introduction The MATLAB colon operator is surprisingly complicated, given that its job seems pretty simple to describe: generate a vector of regularly-spaced values, with a specified starting point, step size, and endpoint. For example, to create the vector : At … Continue reading

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Computing the angle between two vectors

Introduction Given two vectors in three dimensions, what is the most accurate way to compute the angle between them? I have seen several different approaches to this problem recently in the wild, and although I knew some of them had … Continue reading

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Ambiguous notation for logarithms

The motivation for this post is to respond to some questions about a recent video presentation titled, “Why you haven’t caught Covid-19 [sic],” presented by Anne Marie Knott, a professor in the Washington University St. Louis Olin Business School. The … Continue reading

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Sliding rooks (and queens)

Introduction Jacob Brazeal describes the following interesting puzzle in a recent MAA article (see reference below): starting with four rooks in the four corner squares of a chessboard, as shown in the figure below, move the rooks into the four … Continue reading

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