document.write( "Question 1208133: a digital timer counts down from 3 min to zero, one second at a time. for how many seconds does atleast one of these digits show a 5? \n" ); document.write( "

Algebra.Com's Answer #846328 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "It appears that tutor @ikleyn solved the problem for a timer which counts down from 180 seconds to 0 seconds.

\n" ); document.write( "My guess is that the timer counts down from 3:00 to 0:00. In that case....

\n" ); document.write( "The digit for the minutes is never 5.

\n" ); document.write( "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).

\n" ); document.write( "In each minute, the digits representing the seconds contain at least one 5 for the following numbers of seconds:
\n" ); document.write( "59 through 50 (10 occurrences)
\n" ); document.write( "45, 35, 25, 15, and 05 (5 occurrences)

\n" ); document.write( "Total number of times in each minute that at least one of the digits is 5: 10+5 = 15.

\n" ); document.write( "Number of times in 3 minutes that at least one of the digits is 5: 15*3 = 45.

\n" ); document.write( "ANSWER: 45

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