Posted on Categories Expository Writing, math programming, Mathematics, TutorialsTags , , , ,

Unspeakable bets: take small steps

I was watching my cousins play Unspeakable Words over Christmas break and got interested in the end game. The game starts out as a spell a word from cards and then bet some points game, but in the end (when you are down to one marker) it becomes a pure betting game. In this article we analyze an idealized form of the pure betting end game. Continue reading Unspeakable bets: take small steps

Posted on Categories Expository Writing, MathematicsTags , , , ,

Some puzzles about boxes

This article is a break from data-science, and is instead about the kind of problem you can try on the train. It is problem 70 in Bollobas’s “The art of mathematics” (though I forgot that and re-worked the problem crudely from memory when writing this article).

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One of the many irritating things about airlines is the fact that the cary-on bag restrictions are often stated as “your maximum combined linear measurement (length + width + height) must not exceed 45 inches” when they really mean your bag must fit into a 14 inch by 9 inch by 22 inch box (so they actually may not accept a 43 inch by one inch by one inch pool spear as your carry-on). The “total linear measure” seems (at first glance) “gameable,” but can (through some hairy math) at least be seen to at least be self-consistent. It turns out you can’t put a box with longer total linear measurements into a box with smaller total linear measurements.

Let’s work out why this could be problem and then why the measure works. Continue reading Some puzzles about boxes