Sunday Times Teaser 2879 – Blood Line

by Danny Roth

Published November 26 2017 (link)

Patients numbered 1 to 99 were waiting for a blood test. George’s and Martha’s numbers were consecutive. Patients were called in random order to one of the available cubicles numbered 1 to 9. The nurse in each cubicle took a fixed whole number of minutes to do the test, but that time varied from cubicle to cubicle. All cubicles started at 10am and they all finished together before 5pm on the same day. Amazingly, it turned out that each patient’s cubicle number was the highest digit that divided into their patient number. George noted that, when he was called, the session had been running for a number of minutes whose digits added to his cubicle number. Martha noted that the same was true for her.

What were their patient numbers?