Qa09 clock calendar
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This document provides information about determining the day of the week for any given date using the Doomsday algorithm. It explains that certain dates like February 28th, April 4th, June 6th etc. always fall on the same day of the week each year. It then gives the anchor days and memorable rules for determining the day of the week for dates in different centuries from 1800-2199. Specific dates and mnemonics are provided for each month to help with remembering which dates have the same day of the week each year.
![• As mentioned above, the last day of February always falls on the
doomsday, as do the double dates 4/4, 6/6, 8/8, 10/10, and 12/12.
• Four of the odd month dates (May 9, September 5, July 11, and November
7) can be remembered with the mnemonic "I work from 9 to 5 at the 7-
11."
• For March, one can remember the pseudo-date "March 0", which refers to
the day before March 1, i.e. the last day of February; one can alternately
remember the date a week later, March 7, or March 21 which is
traditionally regarded as the first day of spring in the northern hemisphere
and autumn in the southern hemisphere (although after 2007 the
Northward equinox will not fall on that date in Europe again until 2102).[6]
• For January, January 11 is a Doomsday during leap years, while January 10
is a Doomsday during common years; January 3 is a doomsday during
common years and January 4 a Doomsday during leap years, which can be
remembered as "the 3rd during 3 years in 4, and the 4th in the 4th".](https://image.slidesharecdn.com/qa09clockcalendar-130911231842-phpapp01/85/Qa09-clock-calendar-23-320.jpg)
Qa09 clock calendar
- 1. QA09 CLOCK
- 2. • A clock has 2 hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand. • The face of a clock is a circle which subtends an angle of 360° at the centre
- 3. • In every hour (a) Both the hands coincide once. At this point the angle between them is 0°. (b)The hands are straight (point in opposite directions) once. At this point the angles between them are 180°. (c) The hands are twice perpendicular to each other. At this point the angle between them is 90°.
- 5. • When the two hands are at right angles, they are15min spaces apart. • When the two hands are in opposite directions, they are 30 min spaces apart. • In 60 min the minute hand gains 55 min on the hour hand.
- 6. • The minute hand moves 12 times as fast as the hour hand. • Too Fast: If a clock indicates 4 : 30, when the correct time is 4:20, it is said to be 10 min too fast. • Too Slow: If a clock indicates 7 : 30, when the correct time is 7: 45 , it is said to be 15 min too slow.
- 8. • Q2: A watch which gains uniformly is 4 min slow at 7 pm on Monday and is 4 min 24 s fast at 7 pm on following Monday. • When was the watch correct ? • Solution. • Total time in hours from Monday at 7 pm to the following Monday at 7 pm = (7 × 24 ) = 168 hours. • In 168 hours the watch gains : (4+(22/5)) = 42/5mins • Then 4 mins are gained in = ((168× (5/42) × 4 )= 80 hours = 3days and 8 hours. • Watch is correct 3 days and 8 h after 7 pm Monday • i.e, it will be correct at 3 am on Friday.
- 9. • Q3 :How many times in a day, are the hands of a clock in straight line but opposite in direction? • Solution: • The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. • (Because between 5 and 7 they point in opposite directions at 6 o clock only). • So, in a day, the hands point in the opposite directions 22 times.
- 10. • If you look at a clock and the time is 3:15. • What is the angle between the hour and the minute hands? • At 3:15 minute hand will be perfectly horizontal pointing towards 3. Whereas hour hand will be towards 4. • Also, hour hand must have covered 1/4 of angle between 3 and 4. • The angle between two adjacent digits is 360/12 = 30 degrees. • Hence 1/4 of it is 7.5 degrees.
- 11. Adding Time • Let's add 1 hr and 35 minutes and 3 hr 55 minutes together. • What you do is this: • make the 1 hr 35 minutes into one number, which will give us 135 and do the same for the other number, 3 hours 55 minutes, giving us 355 • Now you want to add these two numbers together: • 135 • 355 • ____ • 490 • What you need to do to this and all sub totals is add the time constant of 40. • No matter what the hours and minutes are, just add the 40 time constant to the sub total. • 490 + 40 = 530 • so we can now see our answer is 5 hrs and 30 minutes!
- 12. Calendar
- 13. 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.
- 14. Leap Year • (i). Every year divisible by 4 is a leap year, if it is not a century. • (ii). Every 4th century is a leap year and no other century is a leap year. • Note: A leap year has 366 days. • Examples: • 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. • Ordinary Year: • The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.
- 15. Counting of odd days • 1 ordinary year = 365 days = (52 weeks + 1 day.) • 1 ordinary year has 1 odd day. • 1 leap year = 366 days = (52 weeks + 2 days) • 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. • 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.
- 16. Day of the Week Related to Odd Days No. of days: 0 1 2 3 4 5 6 Day: Sun. Mon. Tues. Wed. Thurs. Fri. Sat.
- 17. • If 6th March 2005 is Monday, what was the day of the week on 6th March, 2004? • The year 2004 is a leap year. So, it has 2 odd days. • But Feb 2004 not included because we are calculating from March 2004 to March 2005. • So it has 1 odd day only. • The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004. • Given that, 6th March, 2005 is Monday, 6th March, 2004 is Sunday • (1 day before to 6th March, 2005.)
- 18. • On what dates of April, 2001 did Wednesday fall? • We shall find the day on 1st April,2001. • 1st April 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001) • Odd days in 2000 years = 0 • Jan,Feb,Mar,Apr • (31+28+31+1) = 91 days = o odd days. • Total number of odd days = 0. • On 1st April 2001 it was Sunday. • In April 2001, Wednesday falls on 4th,11th,18th and 25th.
- 19. • The last day of a century cannot be? • 100 years contain 5 odd days. • Last day of 1st century is Friday. • 200 years contain (5x2) 3 odd days. • Last day of 2nd century is Wednesday. • 300 years contain (5x3) 1 odd day. • Last day of 3rd century is Monday. • 400 years contain 0 odd day • Last day of 4th century is Sunday. • This cycle is repeated. • Hence Last day of a century cannot be Tuesday or Thursday or Saturday.
- 20. • On 8th Feb, 2005 it was Tuesday. • What was the day of the week on 8th Feb 2004? • The year 2004 is a leap year. It has 2 odd days. • The day on 8th Feb 2004 is 2 days before the day on 8th Feb.2005. • Hence this day is Sunday.
- 21. JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 0 3 3 6 1 4 6 2 5 0 3 5 Step1: Ask for the Date. Ex: 23rd June 1986 Step2: Number of the month on the list, June is 4. Step3: Take the date of the month, that is 23 Step4: Take the last 2 digits of the year, that is 86. Step5: Find out the number of leap years. Divide the last 2 digits of the year by 4, 86 divide by 4 is 21. Step6: Now add all the 4 numbers: 4 + 23 + 86 + 21 = 134. Step7: Divide 134 by 7 = 19 remainder 1. The reminder tells you the day. No. of days: 0 1 2 3 4 5 6 Day: Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 1600/2000 1700/2100 1800/2200 1900/2300 0 6 4 2
- 22. • 4/4, 6/6, 8/8, 10/10, 12/12, and the last day of February all occur on the same day of the week in any given year. Applying the Doomsday algorithm involves three steps: • Determine the "anchor day" for the century. • Use the anchor day for the century to calculate the doomsday for the year. • Choose the closest date out of the ones that always fall on the doomsday (e.g. 4/4, 6/6, 8/8), and count the number of days (modulo 7) between that date and the date in question to arrive at the day of the week. • This technique applies to both the Gregorian calendar A.D. and the Julian calendar, although their doomsdays will usually be different days of the week. • Since this algorithm involves treating days of the week like numbers modulo 7, John Conway suggests thinking of the days of the week as "Noneday" or "Sansday" (for Sunday), "Oneday", "Twosday", "Treblesday", "Foursday", "Fiveday", and "Six-a-day".
- 23. • As mentioned above, the last day of February always falls on the doomsday, as do the double dates 4/4, 6/6, 8/8, 10/10, and 12/12. • Four of the odd month dates (May 9, September 5, July 11, and November 7) can be remembered with the mnemonic "I work from 9 to 5 at the 7- 11." • For March, one can remember the pseudo-date "March 0", which refers to the day before March 1, i.e. the last day of February; one can alternately remember the date a week later, March 7, or March 21 which is traditionally regarded as the first day of spring in the northern hemisphere and autumn in the southern hemisphere (although after 2007 the Northward equinox will not fall on that date in Europe again until 2102).[6] • For January, January 11 is a Doomsday during leap years, while January 10 is a Doomsday during common years; January 3 is a doomsday during common years and January 4 a Doomsday during leap years, which can be remembered as "the 3rd during 3 years in 4, and the 4th in the 4th".
- 24. Month Memorable date Month/Day Mnemonic January January 3 (common years), January 4 (leap years) January 11 (leap years) 1/3 or 1/4 1/11 the 3rd 3 years in 4 and the 4th in the 4th all ones February February 14 (common years) February 22 (leap years) February 28 (common years), February 29 (leap years) 2/14 2/22 2/28 or 2/29 Valentine's Day all twos last day of February March "March 0" March 14 March 21 3/0 3/14 3/21 last day of February Pi day traditionally first day of spring/autumn April April 4 4/4 even month May May 9 5/9 9-to-5 at 7-11 June June 6 June 20 6/6 6/20 even month traditionally first day of summer/winter
- 25. July July 4 July 11 7/4 7/11 Independence Day (United States) 9-to-5 at 7-11 August August 8 8/8 even month September September 5 9/5 9-to-5 at 7-11 October October 10 October 31 10/10 10/31 even month Halloween November November 7 11/7 9-to-5 at 7-11 December December 12 December 26 12/12 12/26 even month Boxing Day
- 26. Century Anchor day Mnemonic Index (day of week) 1800–1899 Friday - 5 (Fiveday) 1900–1999 Wednesday We-in-dis-day (most living people were born in that century) 3 (Treblesday) 2000–2099 Tuesday Y-Tue-K or Twos- day (Y2K was at the head of this century) 2 (Twosday) 2100–2199 Sunday Twenty-one-day is Sunday (2100 is the start of the next century) 0 (Noneday) We first take the anchor day for the century. For the purposes of the Doomsday rule, a century starts with '00 and ends with '99. The following table shows the anchor day of centuries 1800–1899, 1900–1999, 2000– 2099 and 2100–2199.
- 27. Month Dates Week numbers * January (common years) 3, 10, 17, 24, 31 1–5 January (leap years) 4, 11, 18, 25 1–4 February (common years) 7, 14, 21, 28 6–9 February (leap years) 1, 8, 15, 22, 29 5–9 March 7, 14, 21, 28 10–13 April 4, 11, 18, 25 14–17 May 2, 9, 16, 23, 30 18–22 June 6, 13, 20, 27 23–26 July 4, 11, 18, 25 27–30 August 1, 8, 15, 22, 29 31–35 September 5, 12, 19, 26 36–39 October 3, 10, 17, 24, 31 40–44 November 7, 14, 21, 28 45–48 December 5, 12, 19, 26 49–52