# Sunday Times Teaser 2837 – Back and Forth

*by Danny Roth*

#### Published: 5 February 2017 (link)

George and Martha have a digital 24-hour clock that always displays the time as four digits (eg, 0217). During one lazy weekend George noted two particular times when the four-digit display was palindromic. He calculated the number of minutes from the first of these times to the second and he discovered that the answer was a three-figure palindrome. When he reported all the details to Martha, she commented that the sum of the eleven digits in the three palindromes was also palindromic.

What were the two palindromic times?

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This program considers when there is a corresponding minute for each hour to make a list of palindromic times, and then considers pairs of times from this list that satisfy the remaining conditions.