# Sunday Times Teaser 3802 – In the Swim

*by Nick MacKinnon*

#### Published Sunday October 17 2021 (link)

Expert mathematicians Al Gritham, Ian Tadger, Carrie Over and Tessa Mole-Poynte have a swimming race for a whole number of lengths. At some point during each length (so not at the ends) they calculate that they have completed a fraction of the distance, and at the finish they compare their fractions (all in the lowest terms). Al says, “My fractions have prime numerators, the set of numerators and denominators has no repeats, their odd common denominator has two digits, and the sum of my fractions is a whole number.” Tessa says, “Everybody’s fractions have all the properties of Al’s, but one of mine is closer to an end of the pool than anybody else’s.”

What were Tessa’s fractions?