### Brain Teasers

# Double Digits

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

As an inveterate clock watcher, James glances at his digital watch at random from time to time throughout the day. What is the probability that he will see all the digits reading the same (for example, 4:44) during any single glance? (Assume a typical day, not a day on which daylight savings time changes or anything like that. The watch is set to a 12 hour U.S. format, not a 24 hour European or military format.)

### Hint

How many times does the given occurrence happen in a day? How long do these occurrences last? How long is this compared to a day?### Answer

There are 12 instances in each 24 hour period when a digital clock or watch will show all identical digits. (1:11,2:22,3:33,4:44,5:55 and 11:11, each times two = 12) for exactly a minute each instance. Since there are 1440 minutes (24x60) in a 24 hour period, the probability of James seeing all the same digits in any 24 hour period is 12/1440 = 0.0083 or slightly less than one chance out of a hundred.Practically speaking, however, since most of us are asleep from 11:11 pm through 5:55 am each NIGHT, James PROBABLY did not glance at his watch during the night hours. Suppose that James sleeps 8 hours every day, the most correct answer would then be 6/960, or about 1 chance in 160. If that (or 0.00625) was your answer, give yourself extra credit for not viewing this as strictly a math problem.

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