# Who Wins A Very Boring Basketball Game?

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2022-05-13 08:00:07

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,1 and you may get a shoutout in the next column. Please wait until Monday to publicly share your answers! If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

There are many fractions with a numerator of 1 whose decimal expansions don’t go on to infinitely many decimal places. For example, 1/4 is equivalent to the decimal 0.25, and 1/500 is equivalent to 0.002. However, the decimal expansion of 1/3 is 0.33333 …, a decimal that never terminates.

If you were to add up all these numbers — fractions with a numerator of 1 whose decimal expansions don’t go on forever — what would be the sum? (Note: Before you ask, let’s include the fraction 1/1 in this group.)