Sunday Times Teaser 2635 – Three Sisters

by Nick MacKinnon

A father shared his estate among his three daughters with each getting a fraction of it.

In their simplest form, these fractions had numerators less than 100 and shared a common denominator.

The largest fraction was less than three times the smallest and each fraction recurred after three places when expressed in decimal form (e.g. 0.abcabc…).

Each of the digits 1 to 9 occurred in one of these three decimals.

What were the three fractions?