Posted in arithmetic, logarithms.

Some time ago, someone asked Uncle Colin what the last two digits of $19^{1000}$ were. That caused few problems. However, Mark came up with a follow-up question: how would you estimate $19^{1000}$? I like this question, and set myself some rules: No calculators (obviously) Only rough memorised numbers ($e \approx

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Posted in arithmetic.

There's not much of a story to this post, except for a few curiosities the decimal system throws up (largely as a result of the binomial expansion). Some time ago, I looked at some Fibonacci witchcraft: $\frac{1}{999,998,999,999} = 0.000\,000\, 000\,001\, 000\,001\, 000\,002\, 000\,003\, 000\,005\, 000\,008\,...$, neatly enumerating the Fibonacci sequence

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Posted in arithmetic.

The following puzzle/trick came up on Futility Closet, one of my favourite sites for recreations. Here's how they describe it: Arrange cards with values ace through 9 in a row, in counting order, with the ace on the left. Take up a card from one end of the row —

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Posted in arithmetic, ask uncle colin.

Dear Uncle Colin, I'm finding it hard to understand why, when you multiply two negative numbers together, you get a positive number. I accept that it's true, but I was brought up to believe that two wrongs don't make a right. -- Positive Equals A Negative Otherwise? There is a

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