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**Clock and Calendar**

Odd Days:

We are supposed to find the day of the week on a given date.

For this, we use the concept of 'odd days'.

In a given period, the number of days more than the complete weeks are called odd days.

- Each of the years 1948, 2004, 1676 etc. is a leap year.
- Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
- None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

The year which is not a leap year is called an ordinary year.

An ordinary year has 365 days.

- 1 ordinary year = 365 days = (52 weeks + 1 day.)
- Therefore, 1 ordinary year has 1 odd day.
- 1 leap year = 366 days = (52 weeks + 2 days)
- Therefore, 1 leap year has 2 odd days.
- 100 years => 76 ordinary years + 24 leap years => (76 x 1 + 24 x 2) odd days = 124 odd days. => (17 weeks + days) 5 odd days.
- Therefore, Number of odd days in 100 years = 5.
- Number of odd days in 200 years = (5 x 2)3 odd days.
- Number of odd days in 300 years = (5 x 3)1 odd day.
- Number of odd days in 400 years = (5 x 4 + 1)0 odd day.
- Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

- 0 - Sun
- 1 - Mon
- 2 - Tues
- 3 - Wed
- 4 - Thurs
- 5 - Fri
- 6 - Sat

- In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.
- In every hour, both the hands coincide once.
- The hands are in the same straight line when they are coincident or opposite to each other.
- When the two hands are at right angles, they are 15 minute spaces apart.
- When the hands are in opposite directions, they are 30 minute spaces apart.
- Angle traced by hour hand in 12 hrs = 360°
- Angle traced by minute hand in 60 min. = 360°.
- If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast. On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

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