Question

A long time ago, Julius and Augustus were trying to renew the calendar system. They got into an argument. They couldn't agree on how many days should be there in a month. According to Augustus, a number should be possible to be constructed from any date of the year by adding the number of the month to the number of the day. with that logic, December 21st would become the number 33, since December is the twelfth month, and 21 + 12 = 33. March 23 would become 26, and so on. Hearing this, Julius was a puzzle. He wondered how many different numbers can be made using dates of a regular calendar. What would be the number?​

Answer 1

Given :  number should be possible to be constructed from any date of the year by adding the number of the month to the number of the day. with that logic, December 21st would become the number 33, since December is the twelfth month, and 21 + 12 = 33. March 23 would become 26, and so on.

To Find :how many different numbers can be made using dates of a regular calendar.

a. 28

b. 34

c. 42

d. 18​

Solution:

January  has 1 to 31 days and month 1  Hence

from 2 to 32

December has  1 to 31 days month 12 Hence

from from 12 to 43

Hence all possible numbers are from

2 to 43

Which counts to be 42

Hence 42 is correct answer

42 different numbers can be made using dates of a regular calendar.

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Answer 2

Given :- December 21st would become the number 33, since December is the twelfth month, and 21 + 12 = 33. March 23 would become 26 .

To Find :-

• How many different numbers can be made using dates of a regular calendar. ?

Solution :-

we know that,

• First month = January = 31 days .
• Last month = 12th month = December = 31 days.

so, according to given logic we get,

→ 1 Jan = 1 + first month = 1 + 1 = 2

→ 31 Jan = 31 + first month = 31 + 1 = 32

Similarly,

→ 1 feb = 1 + 2nd month = 3

→ 28/29 feb = 28 + 2 / 29 + 2 = 30/31

and,

→ 1 march = 1 + 3rd month = 1 + 3 = 4

→ 31 march = 31 + 3 = 34

Conclusion :-

• First number is = 2 (1 Jan)
• Numbers are increasing as 32,33,34, based in numbers of days in months .

then,

→ 31 december = 31 + 12 = 43

we can say that, numbers starts from 2 and ends in 43 .

therefore,

→ Total numbers = 43 - 2 + 1(2 is included) = 42 Numbers (Ans.)

Hence, 42 different numbers can be made using dates of a regular calendar.

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