How would you go about adding up all the integers from 1 to 100? Tap them into a calculator? Write a little computer code? Or look up the general formula for summing integers?

The number 1 can be written as a sum of unit fractions, that is fractions with 1 in the numerator. But how long can we make such a sum?

Runner up in the schools category Being good at mental arithmetic isn't going to gain you much street cred these days. But, as Owen Daniel explains, not so long ago it was a sure route to fame and fortune — even if you were a horse.