Sunday Times Teaser 2752 – Best Before
by Nick MacKinnon
Published: 21 June 2015 (link)
Peter likes to note “pandigital” times, such as 15.46, 29/03/78, that use all ten digits. Here the five individual numbers (15, 46, 29, 3 and 78) have a product that is divisible by the perfect square 36, and they also have a sum that is two more than a perfect square. He has been watching for pandigital times ever since and remembers one where the product of the five numbers was not divisible by any perfect square (apart from 1!): this has never happened since! He is also looking out for a pandigital time where the sum of the five numbers is a perfect square
(a) When was that last “non-square” pandigital time?
(b) When will that first “square-sum” pandigital time be?