How many times does a palindromic number appear on a 12 hour digital clock between 12 midnight and 12 noon?
well at 12 theres one way to get a palindrome and that's 12:21
after that every hour from 1-9 has 6
those are-1:01,1:11, 1:21, 1:31, 1:41, 1:51
the number 1 can be replaced by any number between 1 and 9
then for 10 there is 10:01
for 11 there is 11:11
so we add that all together-
1+(6*9)+2= your answer
57
anyone have this questrion from som?? :p
57
57 duhhhhhhh
uhjs
Yes form som
To find out how many times a palindromic number appears on a 12-hour digital clock between 12 midnight and 12 noon, we need to identify the palindromic numbers that can be represented on the clock.
A palindromic number is a number that remains the same when its digits are reversed. In the case of a 12-hour digital clock, the digits range from 0 to 9.
We can break down the time on the 12-hour digital clock as follows:
- The hours can range from 1 to 12.
- The minutes can range from 0 to 59.
- The seconds can range from 0 to 59.
Now, let's consider the possible scenarios for palindromic numbers on the clock:
1. Palindromic hours:
- The first digit of the hour can range from 1 to 9.
- The second digit of the hour should be the same as the first digit.
- This gives us a total of 9 possible palindromic hour options, from 1:01 to 9:09.
2. Palindromic minutes:
- The first digit of the minutes can range from 0 to 5.
- The second digit of the minutes should be the same as the first digit.
- This gives us a total of 6 possible palindromic minute options, from 10:01 to 50:05.
3. Palindromic seconds:
- The first digit of the seconds can range from 0 to 5.
- The second digit of the seconds should be the same as the first digit.
- This gives us a total of 6 possible palindromic second options, from 10:10:01 to 50:50:05.
To determine the overall count, we need to multiply the possibilities for each scenario:
9 (palindromic hours) * 6 (palindromic minutes) * 6 (palindromic seconds) = 324.
Therefore, there are 324 times that a palindromic number appears on a 12-hour digital clock between 12 midnight and 12 noon.