Edit made on December 05, 2008 by ColinWright at 13:20:33
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!_ To Find out the Day of the Week of any Day _
You need to remember
* a magic number per month, and
* a magic number per century
** (although for the 1900's the magic number is 0.)
Now add together
* the date,
* the year,
* the year divided by 4,
* the magic number for the month,
* the magic number for the century,
and there might be a correction.
Magic Month No. *
| January | 1 | 4 | 4 | March |
| April | 0 | 2 | 5 | June |
| July | 0 | 3 | 6 | September |
| October | 1 | 4 | 6 | December |
Magic Century No.**
| 1700 - 1799 | 4 |
| 1800 - 1899 | 2 |
| 1900 - 1999 | 0 |
| 2000 - 2099 | 6 |
| 2100 - 2199 | 4 |
Let's do 29th April, 1951.
| Day | 29 |
| Year (last 2 digits) | 51 |
| ¼ of year (forget any remainder) | 12 |
| Magic Month Number* | 0 |
| Magic Century Number** | 0 |
| (-1 if Jan/Feb of Leap Year) | 0 |
| TOTAL B = | 92 |
Now divide your total by 7, and keep the remainder.
Our total was 92, which is a multiple of 7 with 1 remainder. _
Hence 29th April 1951 was a Sunday
| Remainder | Day of the Week |
| |>> 1 <<| | Sunday |
| |>> 2 <<| | Monday |
| |>> 3 <<| | Tuesday |
| |>> 4 <<| | Wednesday |
| |>> 5 <<| | Thursday |
| |>> 6 <<| | Friday |
| |>> 0 <<| | Saturday |
* Using modular arithmetic (mod 7) and a reasonable memory can make this method accessible to mental calculation in a reasonable time so as to perform this as a party trick.
* Using modulo arithmetic (mod 7) and a reasonable memory can make this method accessible to mental calculation in a reasonable time so as to perform this as a party trick.
** adding 51 is the same as adding 2 in modulo 7 arithmetic
* In modular arithmetic (mod 7) adding 6 is the same as subtracting 1, which could be easier for mental calculation.
* In modulo arithmetic (mod 7) adding 6 is the same as subtracting 1, which could be easier for mental calculation.
* Some conjurers/memory experts who use this as part of their performance will remember a magic year number for many of the last 100 years.
** Magic year number = [year + ¼ of year (forget any remainder)] mod 7
* For the purposes of this calculation the century starts in years ending in 00.
** e.g. 2000 is considered to be in the 21st Century
* Years ending in 00 are normally not leap years except those which are divisible by 400
** e.g. 1900 was not a leap year but 2000 was a leap year.
* Calculating the day of the week for England before 14th September 1752 is problematic because of the change from the Julian to the Gregorian calendar.
** Isaac Newton would have considered himself to have been born on Christmas Day of 1642 however most present day chronicles will quote his birthday as 4th January 1643.
This is one of the many Enrichment tasks on this site.