MathDB
2019 BMT Individual 14

Source:

January 9, 2022
number theory

Problem Statement

On a 2424 hour clock, there are two times after 01:0001:00 for which the time expressed in the form hh:mmhh:mm and in minutes are both perfect squares. One of these times is 01:2101:21, since 121121 and 60+21=8160+21 = 81 are both perfect squares. Find the other time, expressed in the form hh:mmhh:mm.