Difference between revisions of "2021 JMPSC Sprint Problems/Problem 19"
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| + | ==See also== | ||
| + | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||
| + | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||
| + | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
| + | {{JMPSC Notice}} | ||
Latest revision as of 16:15, 11 July 2021
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. 
