Only Time Will Tell

Apr 30, 2011

RAY: This is from my Play by the Number Series, and it was submitted by Paul Muelick.

These days, almost every car on the road has a digital clock, which gives the hour and the minute, but not the second. At various times of day, such as five minutes before six, the clock will display three of the same digit. For example 5:55.

Here's the question: How many times during the course of a complete day (24-hours) does a car's digital clock display a time that has three of the same digit?
RAY: Here's the answer. Most people I've given this to have gotten the wrong answer. The obvious ones are 2:22, 3:33, 4:44, and 5:55. But let's start at noon time, shall we?

TOM: Yeah.

RAY: OK, if we start at noon, we clearly don't have anything at noon. The first one is 12:11. There are three ones. I didn't say that only three numbers are repeated, but three. Right? So 12:11 has three ones and 12:22 has three twos. And the next one is 1:11, 2:22, 3:33, 4:44, the of course aforementioned 5:55, and then nothing happens for a long time, until 10:00, and that's one that a lot of people miss. 10:00 has three zeroes.

TOM: Oh, of course.

RAY: And then, of course, there's 10:11 and then 11:01. And here's one that people miss all the time, 11:10. And then of course, 11:11 has four, but even though it has four, it has three, right?

TOM: Yeah.

RAY: And then 11:12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 31, 41, 51, and that adds up to 24. So from 12 noon to 12 midnight, we've got 24. So in a 24-hour period, we have 48. Pretty cute, huh? Do we have a winner?

TOM: It is pretty cute. Our winner this week is Jeff Morehouse from Juneau, Alaska. Congratulations, Jeff!

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