Author Archives: possiblywrong

Anagrams

Introduction This was a fun exercise, motivated by several interesting recent posts by Mark Dominus at The Universe of Discourse about finding anagrams of individual English words, such as (relationships, rhinoplasties), and how to compute a “score” for such anagrams by some reasonable … Continue reading

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Array resizing in MATLAB

I encountered the following MATLAB code recently, simplified for this discussion; it builds a 3-by-4-by-2 array by assigning each of its three 4-by-2 “block” sub-arrays in turn to an initially empty array: As this example shows, MATLAB allows resizing arrays on … Continue reading

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Guess the number

I haven’t posted a puzzle in a while.  The following problem has the usual nice characteristics; it works on a cocktail napkin or as a programming problem, via exact solution or simulation, etc. I am thinking of a randomly selected … Continue reading

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Probability of a Scrabble bingo

My wife and I have been playing Scrabble recently.  She is much better at the game than I am, which seems to be the case with most games we play.  But neither of us are experts, so that bingos— playing all … Continue reading

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Risk of (gambler’s) ruin

Suppose that you start with an initial bankroll of dollars, and repeatedly make a wager that pays $1 with probability , and loses $1 with probability .  What is the risk of ruin, i.e., the probability that you will eventually go … Continue reading

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A harder birthday problem

It is a well-known non-intuitive result that in a group of people– conveniently the size of a classroom of students– the probability is at least 1/2 that or more of them share a birthday.  This is a nice problem for several … Continue reading

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Strong induction

What is the best way to explain induction to a student?  That is, given a true-or-false statement involving a natural number , we would like to prove that the statement is true for all such .  How does one prove such … Continue reading

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