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?