2021 JMPSC Sprint Problems/Problem 19
Problem
As an April Fool’s prank, Sean hacks his teacher’s digital clock and switches each digit to a certain letter. Right now, the hacked clock displays .
minutes later, it displays
. If no two digits represent the same letter, find the value of
Solution
Note that if the changes to
in just 14 minutes,
is at the end of an hour, meaning that
is either
or
. If
, T must be
if
minutes later is a new hour. However, at time
minutes after
will be
instead of a new hour number. Thus,
. If in
minutes it is due to be
, then it is between 4-o'clock and 5-o
'clock currently. Thus, from
,
. From
(
), we can guess that
. Then we have
and
. Checking, the times are indeed 14 minutes apart! We want
, so the answer is
.
~MathHayden
(wow this is my *one* actual contribution to the AoPS wiki!)
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.