Discussion
Suppose you have a 12-hour digital clock where the number representing the hour is always the same as the number representing the minute. That is, the clock can only show times like 8:08, 9:09, 10:10, etc. What is the smallest time difference between two such times ?
Answer: D
The smallest time difference is 49 minutes.
On a 12-hour clock the only possible times are 1:01, 2:02, ..., 9:09, 10:10, 11:11 and 12:12. Each step from one hour to the next adds one hour and one minute, so most neighbouring pairs are 61 minutes apart.
The exception is the change from 12:12 back to 1:01:
\[ \begin{aligned} 12{:}12 \to 1{:}00 &= 48 \text{ min} \\ 1{:}00 \to 1{:}01 &= 1 \text{ min} \\ \text{total} &= 49 \text{ min} \end{aligned} \]
61 minutes is the usual gap, not the smallest. 60 minutes would need the minute digits to stay the same, which the rule does not allow, and 101 minutes is not a gap between any two such times.
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