Question 1208133
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It appears that tutor @ikleyn solved the problem for a timer which counts down from 180 seconds to 0 seconds.<br>
My guess is that the timer counts down from 3:00 to 0:00.  In that case....<br>
The digit for the minutes is never 5.<br>
As the timer counts down, the digits representing the numbers of seconds repeat the same sequence in each minute, so we can count the number of times that a 5 appears as either of those digits in one minute and multiply our answer by 3 (for minutes digit 2, 1, or 0).<br>
In each minute, the digits representing the seconds contain at least one 5 for the following numbers of seconds:
59 through 50 (10 occurrences)
45, 35, 25, 15, and 05 (5 occurrences)<br>
Total number of times in each minute that at least one of the digits is 5: 10+5 = 15.<br>
Number of times in 3 minutes that at least one of the digits is 5: 15*3 = 45.<br>
ANSWER: 45<br>