Month: December 2018

Tangents Without Calculus

I always like solving advanced problems with basic methods. For example, many problems that we usually think of as “algebra problems” can be solved by creative thinking without algebra; and some “calculus problems” can be solved using only algebra or geometry. Using simple tools for a big job requires more thought than using “the right …

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Zero Divided By Zero: Undefined and Indeterminate

Back in January, I discussed the issue of division by zero. There is a special case of that that causes even more trouble, in every field from arithmetic to calculus: zero divided by zero. I’ll look at several typical questions that we answered at different levels. Conflicting rules for division? Let’s start here: Zero Laws …

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How Many Different Meals Are Possible?

(An archive question of the week) While gathering combinatorics questions, there were several that stood out. This one will serve well to summarize the topic, showing multiple methods for counting, and contrasting other kinds of problems. The problem The question, from 2007, relates to an Arby’s promotion: How Many Different Dinners Can Be Ordered? I …

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Stars and Bars: Counting Ways to Distribute Items

We have been looking at ways to count possibilities (combinatorics), including a couple ways to model a problem using blanks to fill in. Today, we’ll consider a special model called Stars and Bars, which can be particularly useful in certain problems, and yields a couple useful formulas. (I only remember the method, not the formulas.) …

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