by Graham Smithers
Published May 6 2018 (link)
Several friends have birthdays on different days in 2018, each birthday being given as the weekday, the day of the month and the month with the weekday and the month given in alphabetic form (e.g. Sunday 6 May). The weekday and the month are then converted into sets of numbers by converting each letter into upper case and then replacing A by 1, B by 2, C by 3, …, Z by 26.
The number of friends is as large as possible and, for each friend, the day of the month occurs in the number sets for both the weekday and the month and this is also the only number common to both.
How many friends are there and what is the largest number of clear days between consecutive birthdays in 2018?
(Note: this description is a modified version of the original text published by the Sunday Times: see link)