Tag Archives: binary

Post without words #31

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A few words about PWW #30

A few things about the images in my previous post that you may or may not have noticed: As several commenters figured out, the th diagram (starting with ) is showing every possible subset a set of items. Two subsets … Continue reading

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Post without words #30

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A new counting system

0 = t__ough 1 = t_rough 2 = th_ough 3 = through So, for example, trough through tough though though. English is so strange.

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Goldilogs and the n bears

Once upon a time there was a girl named Goldilogs. As she was walking through the woods one day, she came upon a curious, long house. Walking all round it and seeing no one at home, she tried the door … Continue reading

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The wizard’s rational puzzle (solutions, part 2)

At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading

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Efficiency of repeated squaring: another proof

In my previous post I proved that the “binary algorithm” (corresponding to the binary expansion of a number ) is the most efficient way to build using only doubling and incrementing steps. Today I want to explain another nice proof, … Continue reading

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