Clock and Calendar Numbers
On the usual 12-hour clock, there are timings with different patterns.
For example, 4:44, 10:10, 12:21.
1. Try and find out all possible times on a 12-hour clock of each of these types.
possible times for each type on a 12-hour clock:
2. Manish has his birthday on 20/12/2012 where the digits ‘2’, ‘0’, ‘1’, and ‘2’ repeat in that order?
Manish’s birthday forms a unique pattern where the digits repeat in the specific order of '2', '0', '1', and '2'.
This repetition of digits can be used to find more such dates by identifying other years with
3. Find some other dates of this form from the past?
You can find other dates where the digits repeat in a specific pattern such as:
4. His sister, Meghana, has her birthday on 11/02/2011 where the digits read the same from left to right and from right to left.
This is a palindromic date where the digits form the same pattern when read forward and backward (11/02/2011).
Other examples of such palindromic dates could include:
5. Find all possible dates of this form from the past.
Possible palindromic dates could be:
6. Jeevan was looking at this year’s calendar. He started wondering,“Why should we change the calendar every year? Can we not reuse a calendar?”. What do you think?
Calendars repeat after a specific number of years. A calendar can be reused when the days of the week align again with the dates. This typically happens in cycles of 6, 11, or 28 years, depending on whether
You might have noticed that last year’s calendar was different from this year’s. Also, next year’s calendar will also be
7. Will any year’s calendar repeat again after some years?
8. Will all dates and days in a year match exactly with that of another year?
Not always immediately, but after a certain number of years (like 28 years for leap years), the calendar will exactly match the
1. Pratibha uses the digits ‘4’, ‘7’, ‘3’ and ‘2’, and makes the smallest and largest 4-digit numbers with them: 2347 and 7432. The difference between these two numbers is 7432 – 2347 = 5085. The sum of these two numbers is 9779. Choose 4 -digits to make:
a. the difference between the largest and smallest numbers greater than 5085.
Sol: The largest number that can be formed using the digits would be 7432, and the smallest would be 7234. The difference is
b. the difference between the largest and smallest numbers less than 5085.
Sol: If you consider numbers smaller than 5085, the difference would be between 4732 and 2347, resulting in
c. the sum of the largest and smallest numbers greater than 9779.
Sol: In this case, there are no numbers
d. the sum of the largest and smallest numbers less than 9779.
Sol: The sum of the largest (7432) and smallest (2347) is
2. What is the sum of the smallest and largest 5-digit palindrome? What is their difference?
The smallest 5-digit palindrome is
The sum of these two numbers is
3. The time now is 10:01. How many minutes until the clock shows the next palindromic time? What about the one after that?
The next palindromic time after 10:01 is 11:11. The number of minutes between 10:01 and 11:11 is 70 minutes. The palindromic time after 11:11 would be 12:21, which is
4. How many rounds does the number 5683 take to reach the Kaprekar constant?
To reach the Kaprekar constant (6174), you would perform the subtraction process by rearranging the digits of 5683 from highest to lowest and lowest to highest.
This process typically takes a few rounds, but since the exact steps aren't given here, you would follow the Kaprekar process iteratively until reaching