Page 78 - Ganit Kaushal

Now, follow the steps of the flow chart given above. You will finally reach the Kaprekar number.

A = 8632 A = 6642 A = 7641
B = 2368 B = 2466 B = 1467
C = 8632 – 2368 = 6264 C = 6642 – 2466 = 4176 C = 7641 – 1467 = 6174
(Kaprekar Number)

Readers are advised to start with some more 4-digit numbers and try carrying out these steps, and find
out what happens.
You will always reach the magical Kaprekar number ‘6174’ in at most 7 iterations.
Now, readers are advised to try the ‘Kaprekar procedure’ with a few three-digit numbers, that do not have
all three digits identical.
Do you observe something unique, like a ‘Kaprekar constant’, here as well?
Yes, we do. There is a ‘Kaprekar constant’ for three-digit numbers as well. Try to figure it out.

3.11 CLOCK AND CALENDAR PATTERNS

Having learnt about the various types of angles made by the hands of a clock in the previous chapter, you must
be curious to learn about the amazing patterns found in clocks and calendars. In this section, we will learn
about all these patterns. On a usual 12-hour clock, there are times with different fascinating patterns such as
3:33, 01:01, 12:21, etc.
® Readers are advised to observe and explain these patterns here. Also, find out all possible times on
a 12-hour clock for each of these types.
Vikas, a friend of mine, has his birthday on 20/12/2012. What a
coincidence, he has got such a fascinating pattern in his birthday,
where the digits 2, 0, 1 and 2 repeat in that order.
® Readers are advised to find some other dates of this form from
the past or the future.
Megha has her birthday on 11/02/2011. Amazing, isn’t it?
She has got such a beautiful pattern for her birthday where the
digits read the same from left to right or from right to left. Shall
we call it - A calendar palindrome?
® Readers are advised to write some other dates in this form from the past or the future.

Anuj, my younger brother, was looking at this year’s calendar. He started wondering and came to
me with several mind-boggling questions.
Why should we change the calendar every year?
Can we not reuse a calendar?
Why is it so that last year’s calendar was different from this year, and next year’s calendar is different
from previous years?
Do we always have a different calendar for every year, or will any year’s calendar repeat after some
years?
Will all dates and days in a year match exactly with those of another year?
I told him that the answer to all these questions is very simple. We can count the number of different calendars
if we can take care of just two things.
First — the starting day of each year, that is, from Monday to Sunday.

Second — a leap and a non-leap year.

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