1999 CEMC Pascal Problems/Problem 12

Problem

The time on a digital clock is $5:55$ . How many minutes will pass before the clock next shows a time with all digits identical?

$\text{ (A) }\ 71 \qquad\text{ (B) }\ 72 \qquad\text{ (C) }\ 255 \qquad\text{ (D) }\ 316 \qquad\text{ (E) }\ 436$

Solution

$6$ , $7$ , $8$ , and $9$ can't be used because there are $60$ minutes in an hour. This means that the next time must be $11:11$ .

The time that passes from $5:55$ to $11:00$ is $5$ hours and $5$ minutes long, so the time that passes from $5:55$ to $11:11$ is $5$ hours and $5 + 11 = 16$ minutes long.

Converting this time into minutes, we can see that $5 \times 60 + 16 = 300 + 16 = \boxed {\textbf {(D) } 316}$ minutes will pass.

~anabel.disher

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1999 CEMC Pascal Problems/Problem 12

Problem

Solution