## The Game of Set

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…

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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…

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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…

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Abstract Unit, Algebra, Arenas of mathematical mastery, Mathematics

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…

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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…

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Algebra, Arenas of mathematical mastery, GeoGebra, Geometry, Mathematics

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…

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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…

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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…

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I have borrowed from a colleague a copy of G. A. Wentworth’s Plane and Solid Geometry, copyright 1899 and published 1902 by The Athenæum Press of Boston. I enjoy reading old textbooks because they either reinforce or give lie to certain…

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Here’s a quick one: All rational numbers except 0 can be expressed as \[(-1)^s \Pi p_i^{n_i}\] where \(s \in \{0, 1\}\), \(p_i\) is a prime number, and \(n_i\) is an integer. This reminds me of the restriction on the definition…

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The version of Geometry most widely taught in high schools in the United States is an amalgam of the two most basic fields of geometry: Synthetic and analytic. The mixing of these two is done in such a way as…

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Algebra, Arenas of mathematical mastery, Geometry, History of Mathematics, Mathematics

It is a persistently popular thing to do on social media to post challenges like this one. I used to be of a mind to be outraged at the abuse of the equal sign: Clearly these are not addition problems!…

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A question in this month’s Mathematics Teacher asks about the range of \(\sin(\sin(x))\). My initial concern about this was over the units of the input and output of the sine function. I’ll summarize those briefly, but this post is about…

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