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[mathjax]The game of Set consists of 81 cards. Each card has one, two, or three identical symbols of one of three shapes (oval, diamond, or squiggle), in one of three colors (red, green, or purple) and one of three textures (solid, hollow, striped). A “set” consists of three cards where each of the four attributes…
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[mathjax]This is an example of a common sort of story problem encountered in standardized tests: “1. A team of five professionals can do a certain job in nineteen days; a team of nine apprentices can do the same job in the same amount of time. Assuming all professionals work at the same rate and all…
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George Santayana famously said, “Those who do not learn history are doomed to repeat it.” Recent political events have stirred up the most famous altercation from one of the darkest times in our government’s history. On the ninth day of June 1954, American TV viewers were watching the thirtieth day of hearings involving the Senate…
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[mathjax]Here’s an extension to the problem in my previous post. Time has run out, and a player is at the free throw line. If he makes the first shot, he gets a second try. If he makes both shots, his team wins; if he misses the first, his team loses. Otherwise, it’s a tie game,…
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During the 2016 Republican National Convention, Scott Baio sat down with MSNBC’s Tamron Hall to discuss a tweet he’d made about Hillary Clinton. The tweet contained a photo of Clinton standing in front of the word “COUNT,” with her head obscuring the “O”; the meme contains text referring to the blocked letter. Baio had also added the…
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[mathjax]At a recent workshop on collaboration, the other participants and I were presented with a version of this problem: Adam hits 60% of his free throws. He gets fouled just before the buzzer, and his team is down by one point. Based on the rules in play, he can shoot up to twice. If he…
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We can build relationships with people so they want to cooperate with us, or we can bully them into compliance. Broadly speaking, these are the two basic approaches authority figures can take to elicit the people’s compliance with rules and expectations: Authoritative or authoritarian. As the father of a small child, a teacher with experience…
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[mathjax]I’ve seen variations of this one a few times, so I thought I’d give it a quick write-up. The simpler version is: Given two circles that are tangent and a line that is cotangent to them, what is the length of the segment between the points of tangency? To make things easier, the radii are…
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[mathjax]Most people are aware of two or three basic tests for divisibility by a prime number: A number n is divisible by 2 iff it ends in an even number (0, 2, 4, 6, or 8) by 5 iff it ends in a 0 or a 5 by 3 iff its digits add up to a multiple of 3 These…
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[mathjax]A recent comment from a colleague got me thinking about describing polygons using functions. His intent was that polygons (and all closed shapes) can be described as sets of functions; for instance, a triangle could be described by three linear functions with the domain of the triangle’s vertices. And, of course, any closed shape cannot…