Thomson scattering
The Doomsday rule or Doomsday algorithm is a way of calculating the day of the week of a given date. It provides a perpetual calendar since the Gregorian calendar moves in cycles of 400 years.
This algorithm for mental calculation was devised by John Conway[1][2] after drawing inspiration from Lewis Carroll's work on a perpetual calendar algorithm.[3][4] It takes advantage of the fact that each year has a certain day of the week (the doomsday) upon which certain easy-to-remember dates fall; for example, 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".
The algorithm is simple enough for anyone with basic arithmetic ability to do the calculations mentally. Conway can usually give the correct answer in under two seconds. To improve his speed, he practices his calendrical calculations on his computer, which is programmed to quiz him with random dates every time he logs on.[5]
Doomsdays for some contemporary years
Doomsday for the current year in the Gregorian calendar (2024)' is '.
For some other contemporary years :
Mon. | Tue. | Wed. | Thu. | Fri. | Sat. | Sun. | Mon. | Tue. | Wed. | Thu. | Fri. | Sat. | Sun. |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
→ | 1944 | 1945 | 1946 | 1947 | → | 1948 | 1949 | 1950 | 1951 | → | 1952 | 1953 | 1954 |
1955 | → | 1956 | 1957 | 1958 | 1959 | → | 1960 | 1961 | 1962 | 1963 | → | 1964 | 1965 |
1966 | 1967 | → | 1968 | 1969 | 1970 | 1971 | → | 1972 | 1973 | 1974 | 1975 | → | 1976 |
1977 | 1978 | 1979 | → | 1980 | 1981 | 1982 | 1983 | → | 1984 | 1985 | 1986 | 1987 | → |
1988 | 1989 | 1990 | 1991 | → | 1992 | 1993 | 1994 | 1995 | → | 1996 | 1997 | 1998 | 1999 |
→ | 2000 | 2001 | 2002 | 2003 | → | 2004 | 2005 | 2006 | 2007 | → | 2008 | 2009 | 2010 |
2011 | → | 2012 | 2013 | 2014 | 2015 | → | 2016 | 2017 | 2018 | 2019 | → | 2020 | 2021 |
2022 | 2023 | → | 2024 | 2025 | 2026 | 2027 | → | 2028 | 2029 | 2030 | 2031 | → | 2032 |
2033 | 2034 | 2035 | → | 2036 | 2037 | 2038 | 2039 | → | 2040 | 2041 | 2042 | 2043 | → |
2044 | 2045 | 2046 | 2047 | → | 2048 | 2049 | 2050 | 2051 | → | 2052 | 2053 | 2054 | 2055 |
→ | 2056 | 2057 | 2058 | 2059 | → | 2060 | 2061 | 2062 | 2063 | → | 2064 | 2065 | 2066 |
2067 | → | 2068 | 2069 | 2070 | 2071 | → | 2072 | 2073 | 2074 | 2075 | → | 2076 | 2077 |
2078 | 2079 | → | 2080 | 2081 | 2082 | 2083 | → | 2084 | 2085 | 2086 | 2087 | → | 2088 |
2089 | 2090 | 2091 | → | 2092 | 2093 | 2094 | 2095 | → | 2096 | 2097 | 2098 | 2099 | 2100 |
Notes: Fill in the table horizontally, skipping one column for each leap year. This table cycles every 28 years, except in the Gregorian calendar on years multiple of 100 (like 1900 which is not a leap year) that are not multiple of 400 (like 2000 which is still a leap year). The full cycle is 28 years (1,461 weeks) in the Julian calendar, 400 years (20,871 weeks) in the Gregorian calendar.
Memorable dates that always land on Doomsday
One can easily find the day of the week of a given calendar date by using a nearby Doomsday as a reference point. To help with this, the following is a list of easy-to-remember dates for each month that always land on the Doomsday.
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".
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 May 30 |
5/9 5/30 |
9-to-5 at 7-11 Traditional Memorial Day (United States) |
June | June 6 June 20 |
6/6 6/20 |
even month traditionally first day of summer/winter |
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 |
Since the Doomsday for a particular year is directly related to weekdays of dates in the period from March through February of the next year, common years and leap years have to be distinguished for January and February of the same year.
Examples
Suppose you want to know which day of the week Christmas Day of 2006 was. In the year 2006, Doomsday was Tuesday. Since December 12 is a Doomsday, December 25, being thirteen days afterwards (two weeks less a day), fell on a Monday.
It's useful to note that Christmas Day is always the day before Doomsday ("One off Doomsday"). In addition, July 4 is always on a Doomsday, and so is Halloween.
Suppose that you want to find the day of week that the September 11, 2001 attacks on the World Trade Center occurred. The century anchor was Tuesday, and Doomsday for 2001 is one day beyond, which is Wednesday. September 5 was a Doomsday, and September 11, six days later, fell on a Tuesday.
Finding a year's Doomsday
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.
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) |
Next, we find the year's Doomsday. To accomplish that according to Conway:
- Divide the year's last two digits (call this y) by 12 and let a be the floor of the quotient.
- Let b be the remainder of the same quotient.
- Divide that remainder by 4 and let c be the floor of the quotient.
- Let d be the sum of the three numbers (d = a + b + c). (It is again possible here to divide by seven and take the remainder. This number is equivalent, as it must be, to the sum of the last two digits of the year taken collectively plus the floor of those collective digits divided by four.)
- Count forward the specified number of days (d or the remainder of d/7) from the anchor day to get the year's Doomsday.
For the twentieth-century year 1966, for example:
As described in bullet 4, above, this is equivalent to:
So Doomsday in 1966 fell on Monday.
Similarly, Doomsday in 2005 is on a Monday:
Why it works
The doomsday calculation is effectively calculating the number of days between any given date in the base year and the same date in the current year, then taking the remainder modulo 7. When both dates come after the leap day (if any), the difference is just 365y plus y/4 (rounded down). But 365 equals 52*7+1, so after taking the remainder we get just
This gives a simpler formula if one is comfortable dividing large values of y by both 4 and 7. For example, we can compute , which gives the same answer as in the example above.
Where 12 comes in is that the pattern of almost repeats every 12 years. After 12 years, we get (12 + 12/4) mod 7 = 15 mod 7 = 1. If we replace y by y mod 12, we are throwing this extra day away; but adding back in compensates for this error, giving the final formula.
The Odd+11 method
A simpler method for finding the year's doomsday was discovered in 2010 by Chamberlain Fong and Michael K. Walters,[7] and described in their paper submitted to the 7th International Congress on Industrial and Applied Mathematics (2011). Called the Odd+11 method, it has been proved[7] equivalent to computing
It is well suited to mental calculation, because it requires no division by 4 (or 12), and the procedure is easy to remember because of its repeated use of the "odd+11" rule.
Extending this to get the Doomsday, the procedure is often described as accumulating a running total T in six steps, as follows:
- Let T be the year's last two digits.
- If T is odd, add 11.
- Now let T = T/2.
- If T is odd, add 11.
- Now let T = 7 − (T mod 7).
- Count forward T days from the century's anchor day to get the year's Doomsday.
Applying this method to the year 1966, for example, the steps as outlined would be:
- T = 66
- T = 66 (Do nothing since T is even.)
- T = 66/2 = 33
- T = 33+11 = 44 (Add 11 because T is odd.)
- T = 7 − (44 mod 7) = 7 − 2 = 5
- Doomsday for 1966 = 5 + Wednesday = Monday
The explicit formula for the odd+11 method is:
Although this expression looks daunting and complicated, it is actually simple[7] because of a common subexpression that only needs to be calculated once.
Dominical letter method
A year's doomsday (DD) can be determined from a year's dominical letter (DL), too.
Note: A = 1, B = 2, ..., G = 0.
For the year 1966 the dominical letter is B, so the doomsday DD = 3 - 2 = 1 = Monday.
Finding a century's anchor day
For the Gregorian calendar:
For the Julian calendar:
Overview of all Doomsdays
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 |
* In leap years the nth Doomsday is in ISO week n. In common years the day after the nth Doomsday is in week n. Thus in a common year the week number on the Doomsday itself is one less if it is a Sunday, i.e., in a common year starting on Friday.
Computer formula for the Doomsday of a year
For computer use, the following formulas for the Doomsday of a year are convenient.
For the Gregorian calendar:
For example, the year 2009 has a doomsday of Saturday under the Gregorian calendar (the currently accepted calendar), since
For the Julian calendar:
The formulas apply also for the proleptic Gregorian calendar and the proleptic Julian calendar. They use the floor function and astronomical year numbering for years BC.
For comparison, see the calculation of a Julian day number.
400-year cycle of Doomsdays
Julian centuries ——— Gregorian centuries \ Years |
-200J 500J 1200J 1900J — -400 0 400 800 1200 1600 2000 2400 |
-100J 600J 1300J 2000J — |
0J 700J 1400J 2100J — -300 100 500 900 1300 1700 2100 2500 |
100J 800J 1500J 2200J — |
200J 900J 1600J 2300J — -200 200 600 1000 1400 1800 2200 2600 |
300J 1000J 1700J 2400J — |
400J 1100J 1800J 2500J — -100 300 700 1100 1500 1900 2300 2700 |
---|---|---|---|---|---|---|---|
00 28 56 84 | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. |
01 29 57 85 | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. |
02 30 58 86 | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. |
03 31 59 87 | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. |
04 32 60 88 | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. |
05 33 61 89 | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. |
06 34 62 90 | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. |
07 35 63 91 | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. |
08 36 64 92 | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. |
09 37 65 93 | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. |
10 38 66 94 | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. |
11 39 67 95 | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. |
12 40 68 96 | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. |
13 41 69 97 | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. |
14 42 70 98 | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. |
15 43 71 99 | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. |
16 44 72 | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. |
17 45 73 | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. |
18 46 74 | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. |
19 47 75 | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. |
20 48 76 | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. |
21 49 77 | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. |
22 50 78 | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. |
23 51 79 | Tue. | Mon. | Sun. | Sat. | Fri. | Thu. | Wed. |
24 52 80 | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. | Fri. |
25 53 81 | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. | Sat. |
26 54 82 | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. | Sun. |
27 55 83 | Sun. | Sat. | Fri. | Thu. | Wed. | Tue. | Mon. |
Since in the Gregorian calendar there are 146097 days, or exactly 20871 seven-day weeks, in 400 years, the anchor day repeats every four centuries. For example, the anchor day of 1700–1799 is the same as the anchor day of 2100–2199, i.e. Sunday.
The full 400-year cycle of Doomsdays is given in the table to the right. The centuries are for the Gregorian and proleptic Gregorian calendar, unless marked with a J for Julian. The Gregorian leap years are highlighted.
Negative years use astronomical year numbering. Year 25BC is −24, shown in the column of −100J (proleptic Julian) or −100 (proleptic Gregorian), at the row 76.
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Total | |
---|---|---|---|---|---|---|---|---|
Non-leap years | 43 | 43 | 43 | 43 | 44 | 43 | 44 | 303 |
Leap years | 13 | 15 | 13 | 15 | 13 | 14 | 14 | 97 |
Total | 56 | 58 | 56 | 58 | 57 | 57 | 58 | 400 |
A leap year with Monday as Doomsday means that Sunday is one of 97 days skipped in the 497-day sequence. Thus the total number of years with Sunday as Doomsday is 71 minus the number of leap years with Monday as Doomsday, etc. Since Monday as Doomsday is skipped across 29 February 2000 and the pattern of leap days is symmetric about that leap day, the frequencies of Doomsdays per weekday (adding common and leap years) are symmetric about Monday. The frequencies of Doomsdays of leap years per weekday are symmetric about the Doomsday of 2000, Tuesday.
The frequency of a particular date being on a particular weekday can easily be derived from the above (for a date from 1 January - 28 February, relate it to the Doomsday of the previous year).
For example, 28 February is one day after Doomsday of the previous year, so it is 58 times each on Tuesday, Thursday and Sunday, etc. 29 February is Doomsday of a leap year, so it is 15 times each on Monday and Wednesday, etc.
28-year cycle
Regarding the frequency of Doomsdays in a Julian 28-year cycle, there are 1 leap year and 3 common years for every weekday, the latter 6, 17 and 23 years after the former (so with intervals of 6, 11, 6, and 5 years; not evenly distributed because after 12 years the day is skipped in the sequence of Doomsdays).Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. The same cycle applies for any given date from 1 March falling on a particular weekday.
For any given date up to 28 February falling on a particular weekday, the 3 common years are 5, 11, and 22 years after the leap year, so with intervals of 5, 6, 11, and 6 years. Thus the cycle is the same, but with the 5-year interval after instead of before the leap year.
Thus, for any date except 29 February, the intervals between common years falling on a particular weekday are 6, 11, 11. See e.g. at the bottom of the page Common year starting on Monday the years in the range 1906–2091.
For 29 February falling on a particular weekday, there is just one in every 28 years, and it is of course a leap year.
Julian calendar
The Gregorian calendar accurately lines up with astronomical events such as solstices. In 1582 this modification of the Julian calendar was first instituted. In order to correct for calendar drift, 10 days were skipped, so Doomsday moved back 10 days (i.e. 3 days): Thursday 4 October (Julian, Doomsday is Wednesday) was followed by Friday 15 October (Gregorian, Doomsday is Sunday). The table includes Julian calendar years, but the algorithm is for the Gregorian and proleptic Gregorian calendar only.
Note that the Gregorian calendar was not adopted simultaneously in all countries, so for many centuries, different regions used different dates for the same day.
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Full examples
Example 1 (1985)
Suppose you want to know the day of the week of September 18, 1985. You begin with the century's anchor day, Wednesday. To this, we'll add three things, called a, b, and c above:
- a is the floor of 85/12, which is 7.
- b is 85 mod 12, which is 1.
- c is the floor of b/4, which is 0.
This yields 8. In modulo 7 arithmetic, 8 is congruent to 1. Because the century's anchor day is Wednesday (index 3), and 3 + 1 = 4, Doomsday in 1985 was Thursday (index 4). We now compare September 18 to a nearby Doomsday, September 5. We see that the 18th is 13 past a Doomsday. In modulo 7 arithmetic, 13 is congruent to 6 or, more succinctly, -1. Thus, we take one away from the Doomsday, Thursday, to find that September 18, 1985 was a Wednesday.
Example 2 (other centuries)
Suppose that you want to find the day of week that the American Civil War broke out at Fort Sumter, which was April 12, 1861. The anchor day for the century was 99 days after Thursday, or, in other words, Friday (calculated as (18+1)*5+floor(18/4); or just look at the chart, above, which lists the century's anchor days). The digits 61 gave a displacement of six days so Doomsday was Thursday. Therefore, April 4 was Thursday so April 12, eight days later, was a Friday.
See also
- Mon - Tue - Wed - Thu - Fri - Sat - Sun – common years with the given Doomsday
- Mon - Tue - Wed - Thu - Fri - Sat - Sun – leap years with the given Doomsday
- Ordinal date
- Computus – Gauss algorithm for Easter date calculation
- Zeller's congruence - An algorithm (1882) to calculate the day of the week for any Julian or Gregorian calendar date.
- Mental calculation
References
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This bought me thinking and I started to surprise – how much does a property agent really earn? We often hear or read about sure brokers making million dollar commissions, however is that the exception or the norm? That piqued my curiosity. Like any job, those who put in time and effort will do well and rise to the top. The ethics of exhausting work apply to the true property market as nicely. For individuals who are pondering of making a career change to develop into a property agent, you should be ready to invest the trouble to do properly. Otherwise you may just add to the statistic of brokers who eventually drop out of the realtor game. Properties that do not fall within the definition of residential properties stated above are non-residential properties Web site - www.riaschool.com.sg
Ought to you are on the lookout for new properties for investment or for own stay, we offer property recommendation and search services tailored to your needs. We have represented many together with worldwide and local buyers in efficiently finishing their property purchases. We work with main builders to bring you the latest and one of the best prime properties in Singapore. We are a one-cease service that may full your property cycle from purchase to sale. Property agents for Singapore Land Authority protecting among the government colonial properties for rent. Property leases for expatriates and foreigners. Also helps expats to purchase and promote their properties as well as property investment opportunities in Singapore and China. The Restaurant Affiliation of Singapore
- Encyclopedia of Weekday Calculation by Hans-Christian Solka, 2010
- Doomsday calculator that also "shows all work"
- World records for mentally calculating the day of the week in the Gregorian Calendar
- What is the day of the week, given any date?
- Doomsday Algorithm
- Finding the Day of the Week
- The minimal educational requirement to take the REA or RES examination is four GCE "" level passes or equal. When you have taken the obligatory preparatory course offered by a CEA Authorised Course Supplier and want to apply for the exam, please click on right here.
In an ordinary Singapore Tenancy Agreement, there is usually the reimbursement clause together with the diplomatic clause. This clause states that in the event you train the diplomatic clause, you will have to reimburse a part of the commission the landlord had paid to his agent. Figures additionally show that the number of property agents registered with the Council for Estate Companies (CEA) The property company watchdog mentioned property agents who did not continue with their registration were part timers Tuas South Road 5 Industrial Website on the market So the right way to be a Real Estate Agent in Singapore? Be registered with just one Licensed Estate Agent (Actual Estate Firm) Abroad Property Analysis Experiences Region Property Consultancy & Management Providers Pte Ltd UE Square (D09) – Residence For Hire
final January. There are also fewer property companies in business, down by 5% to lower than 1,500. Other than passing a compulsory examination, registered property brokers also have to endure six hours of Some business players stated new agents face a tough time juggling this and shutting property deals. With a purpose to make the TA a sound authorized document to be honoured by all parties involved, it must be stamped by the Singapore Inland Revenue Authority (IRA). The costs for this process, a so-known as "stamp obligation", are to be borne by the tenant. Softening in residential property costs proceed, led by 2.8 per cent decline within the index for Remainder of Central Area Freehold improvement in the prestigious Ardmore Park / Claymore district with potential for en bloc sale
An expert property agent in Singapore will assist you and defend your interest all through the purchase, secure the provide for you at the best possible price. With a a lot better data of Singapore, the agent can be in a greater position to recommend and recommendation on the selection of property. He may even ensure that all documents are in order and you might be coping with the rightful owner of the property. Singapore 529508 Contact Leon in OrangeTee or click here to read more if you wish to be property agent – Singapore Real Property Salesperson. Rental estate agent for condominiums, bungalows, semi-detached or public apartments in Singapore. Luxurious condo close to Somerset MRT Condominium For Sale – St Thomas Suites (D09) Singapore Contractors Affiliation Ltd Search
Freehold Condo near Orchard The Edge on Cairnhill – Condominium For Sale One-cease service for expatriate and foreign patrons. Collection of properties for lease and for sale in Singapore. Property brokers for sale or rental of properties assisting property house owners and those searching for properties to rent or buy. Residences, homes and HDB's. Blk 138 Lorong Ah Soo, Singapore 530138. Commercial and residential property real property agents. 31 Scotts Road, Dean's Property Centre, Singapore 228225. Excessive-end apartment in singapore close to Orchard Road Condominium For Sale – Paterson Residence (D09) Property agent / real estate agent coping with leasing, rental, sale and buy of business and residential properties Meet the Manager Singapore Glass Affiliation REMAX Singapore New Launches
Property companies embrace buy, sell or hire properties, financial planning, pattern forecasts, relocation, interior design and actual estate planning. Condominium For Lease – The Balmoral (D10) Shopping for a house is a large funding that calls for much consideration and research. The same applies for selling or renting a property, the place a lot effort and time should be spent in negotiating for supreme prices. To watch itemizing and transacted prices Our mistake was that we didn't have our personal agent. One that could have defined all this to us, why it was needed and so forth. But we still did not realise this at the moment, we just assumed that this agent (named A) was serving to us. Little did we know "A" was truly the homeowners agent and we had no 'declare' on him in any respect.
Vendor Pays the Buyer's Dealer Commission via his itemizing agent. Underneath a Purchaser's Broker arrangement, the named brokerage and agent represent the customer. The price paid to the broker mostly is paid by the vendor. Some buyer dealer agreements include clauses that will compensate the brokerage for the price it's due less the quantity paid by the vendor. When I managed to sell a property for my shopper at double fast time and at a really good worth. The worth was higher than most models being bought at the moment. It was a lot of onerous work and naturally Luck performed an enormous part. The Consumer was very very grateful. Sellers pay a 2% commission. May be decrease for more expensive properties. CONTACTING ME We Will Achieve Your Wants And Desires In Actual Estate
- ↑ John Horton Conway, "Tomorrow is the Day After Doomsday", Eureka, volume 36, pages 28-31, October 1973.
- ↑ Richard Guy, John Horton Conway, Elwyn Berlekamp : "Winning Ways: For Your Mathematical Plays, Volume. 2: Games in Particular", pages 795-797, Academic Press, London, 1982, ISBN 0-12-091102-7.
- ↑ Lewis Carroll, "To Find the Day of the Week for Any Given Date", Nature, March 31, 1887.
- ↑ Martin Gardner, "The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays", pages 24-26, Springer-Verlag, 1996
- ↑ Alpert, Mark. "Not Just Fun and Games", Scientific American, April, 1999.
- ↑ Template:Cite web
- ↑ 7.0 7.1 7.2 Chamberlain Fong, Michael K. Walters: "Methods for Accelerating Conway's Doomsday Algorithm (part 2)", 7th International Congress on Industrial and Applied Mathematics (2011)