Category Archives: Uncategorized

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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Seven riffle shuffles is not enough– except when it is

Introduction How many times should you riffle shuffle a deck of cards? A commonly cited rule of thumb (see [1], as well as here, here, and here) is that seven riffle shuffles are sufficient to randomize a standard 52-card deck. … Continue reading

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History of COVID-19 cases

All of the raw data presented here was retrieved from this GitHub repository, which, as described there, is maintained by and thanks to the Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE), with support by ESRI Living … Continue reading

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Fair dice: some isohedra are less fair than others

Introduction What makes dice fair? Intuitively, when we roll a fair die with sides, we expect each of its possible outcomes to have the same probability of occurring. What shapes have this property? I think this is an interesting problem, … Continue reading

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