Pick the Base

Difficulty: ★ ★ ★ ☆

I watched the film Contact a few weeks ago. The movie is about first contact with an alien civilization. It’s smart cinema, which offers that communications between species would be mathematical in nature, as math is the universal language.
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Emulating the Modulus Operator

Difficulty: ★ ★ ☆ ☆

I think any kid learning math in school knows what a remainder is, but few understand (or are taught) what a modulus is. It obtains the remainder of one value divided by another, specifically a larger value divided by a smaller value. In C programming, the % (modulo) operator performs this calculation. But what if the C language lacked a modulo operator?
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The Double Factorial

Difficulty: ★ ★ ☆ ☆

It’s common in programming to use a factorial as a way to teach about recursion. For example, 5! (five factorial) is 5×4×3×2×1, which is 120. Calculating this result can be done with a recursive function, which is practical and satisfying. But mathematicians have a twisted sense of humor, so they invented something called a double factorial.
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