Sunday Times Teaser 2825 – Twin Sets

by Victor Bryant

Published: 13 November 2016 (link)

The twins Wunce and Repete each made a list of positive perfect squares. In Wunce’s list each of the digits 0 to 9 was used exactly once, whereas in Repete’s list each of the digits was used at least once. Wunce commented that the sum of his squares equalled their year of birth, and Repete responded by saying that the sum of his squares was less than the square of their age [1].

What is the sum of Wunce’s squares, and what is the sum of Repete’s?

[1] “.. in 2018.” was omitted in error here.