The time on a digital clock is 10:25. In minutes, what is the shortest length of time until all the digits on the clock will be equal to one another?
(A) 36
(B) 107
(C) 86
(D) 46
(E) 187
The first time after 10:25 at which all of the digits on the clock will be equal to one another is $11: 11$.

Thus, the shortest length of time required is the elapsed time between 10:25 and 11:11, or 46 minutes (because the time from 10:25 to 11:00 is 35 minutes and the time from 11:00 to 11:11 is 11 minutes).