Sunday Times Teaser 2830 – Time for Christmas

by Danny Roth

Published: 18 December 2016 (link)

For Christmas George has bought Martha a novelty digital 24-hour clock. It has an eight-digit display forming four two-digit numbers. The first three of these two-digit numbers are very conventional – the hours, the minutes and the seconds. However, the final two-digit display shows the sum of the first six displayed digits!

On two occasions today all eight digits displayed were different and three of the four two-digit numbers were perfect squares. Between those two occasions there was a time when the eight digits displayed were again all different, but this time the sum of the eight digits was a perfect square!

What was the eight-digit display at that in-between time?