Ishrat Z.

asked • 09/09/16

problem solving

At how many different times will the digit 7 appear on a digital clock in 24 hours?

1 Expert Answer

By:

Mark M. answered • 09/09/16

Tutor
5.0 (278)

Mathematics Teacher - NCLB Highly Qualified

Ishrat Z.

this is wrong the correct answer is actually 158
Report

09/09/16

Mark M.

Perhaps you shall be kind enough to point out my error?
Report

09/09/16

Ishrat Z.

so for 22 hour (not counting 7am/pm) there are 132 times 7 is shown (6 times every hour and multiply that by 22)
in 7 am/pm it is listed 13 times each so it is 26 times for both hours (7 00, 7 07, 7 17, 7 27, 7 37, 7 47, 7 57) 
after u add those together u get 158
Report

09/09/16

Mark M.

I agree with the calculation for the 22 hours.
For the 7 am/pm would there not be 120? 7:01, 7:02, 7:03, .... twice?
So the total would be 132 + 120 = 252?
Report

09/09/16

David W.

The answer 146 counts all the "time readings" where the 24-hour digital clock changes one of the digits from 6 to 7 then from 7 to 8.  This is assumed to be one count of a 7 appearing (then disappearing).
 
If you count both 7's in 7:07, 7:17, etc. [note: they are both "new" in 7:07, but only one of them is "new" in all the rest of those times], then to be consistent, you should count 7:00, 7:01, 7:02, etc. as different "time readings" where a 7 appears.
 
So, I would say that 158 is never an acceptable answer to this problem.
Report

09/10/16

Mark M.

The condition is "different" times, and 7:01 is different from 7:07.
Report

09/10/16

Ishrat Z.

thank you i believe u r right
Report

09/10/16

Mark M.

You are welcome. 
If you are the one who did a "thumbs down" for my solution, would you kindly remove it?
Thank you.
Report

09/10/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.