# Three Digits

How many times during the course of a complete day does a digital clock display a time that has three of the same digit?

### 20 guesses to Three Digits

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• Dude

Not even close.

Keep trying.

• G

30 forgot one then am&pm

• Dude

No to both.

Keep trying.

• 6 times a day 12 1 2

• Roolstar

2 types of hours during a 24 hour day (and in a 24 hour format digital clock – NO AM-PM with 01:00 format style):

Group A – The hours with 2 equal hour digits: 00:xx 11:xx and 22:xx (3 possibilities)
The clock shows 3 same digits:
6 times every 10 minutes (every time the minute digits equals that of the hour)
+ 9 times during the 10 minutes where the minutes’ tens digit equals to the hour (excluding 1 already counted with the 6 times before)
ex for 11:xx
=> 11:01 – 11:11 – 11:21 – 11:31 – 11:41 – 11:51 (6 times)
and 11:10 – 11:12 – 11:13 – 11:14 – 11:15 – 11:16 – 11:17 – 11:18 – 11:19 (9 times) 11:11 Is already counted

So in all, group A gets us 15 x 3 = 45 times

Group B – The hours with different hour digits (01:xx 02:xx …. 23:xx) (21 possibilities)
The clock shows 3 same digits only twice every hour: when the minutes digits are the same as one of the hour digits
ex for 12:xx
=> 12:11 and 12:22

So in all group B gets us 2 x 21 = 42 times

My answer will then be:

a clock will display AT LEAST 3 same digits 87 times in a day for a digital clock with 2 digit hour in a 24 hours mode
and
a clock will display EXACTLY 3 same digits 84 times in a day for a digital clock with 2 digit hour in a 24 hours mode (excluding 00:00 – 11:11 and 22:22)

Other modes can be deduced by the same logic (I mean with AM-PM clocks or ones with the format 1:43…

For the 1:43 format style (still no AM-PM) the number of times would be 64 times for the AT LEAST 3 digits
and 62 times for the EXACTLY 3 digits condition

Very sorry for the long post, did the best I can to cover all possibilities

• Dude

Very elaborate, but not the answer we were looking for.

Keep trying.

• serrano

12

• serrano

No wait 14

• Dude

LOL Serrano, make up your mind … but no!

• serrano

13

• Dude

No, it’s not 13. List your answers please.

• Roolstar

Could you please specify the clock format?

01:00 or 1:00?
11:00 PM or 23:00?

• Dude

1:00 am and 11:00pm

• Roolstar

In that case 24 times

From 1:00 to 5:00 => 5 times (1:11 – 2:22 – 3:33 – 4:44 – 5:55)
From 6:00 to 9:00 => Never
During 10:00 => 2 times (10:00 – 10:11)
During 11:00 => 15 times (in my pervious post)
During 12:00 => 2 times (12:11 – 12:22)

Total = 12 for half day
24 times in a whole day

• LP3

Please post the answer, I need to know this so bad.

• LP3

PLEASE HELP I MUST KNOW THE ANSWER IS IT 48?!?!?!