Category Archives: Uncategorized

The following are equivalent

I have been reviewing Rosen’s Discrete Mathematics and Its Applications textbook for a course this fall, and I noticed an interesting potential pitfall for students in the first chapter on logic and proofs. Many theorems in mathematics are of the … Continue reading

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Dice puzzle

I recently encountered the following interesting problem: Suppose that I put 6 identical dice in a cup, and roll them simultaneously (as in Farkle, for example).  Then you take those same 6 dice, and roll them all again.  What is … Continue reading

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A number concatenation problem

Introduction Consider the following problem: given a finite set of positive integers, arrange them so that the concatenation of their decimal representations is as small as possible.  For example, given the numbers {1, 10, 12}, the arrangement (10, 1, 12) … Continue reading

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Cutting crown molding

This post captures my notes on how to determine the miter and bevel angles for cutting crown molding with a compound miter saw.  There are plenty of web sites with tables of these angles, and even formulas for calculating them, but … Continue reading

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Iterative Poohsticks

The game of Poohsticks was invented by Milne and appears in one of his books, where Pooh and Christopher Robin each simultaneously drop a stick into a river from the upstream side of a bridge.  The winner is the one … Continue reading

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Horse race puzzle

Introduction This post is part pedagogical rant, part discussion of a beautiful technique in combinatorics, both motivated by a recent exchange with a high school student, about an interesting dice game that seems to be a common introductory exercise in probability: … Continue reading

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The hardest 24 puzzles

Introduction Once again motivated by a series of interesting posts by Mark Dominus, a “24 puzzle” is a set of 4 randomly selected numbers from 1 to 9, where the objective is to arrange the numbers in an arithmetic expression … Continue reading

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