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!_ To Find out the Day of the Week of any Day _ COLUMN_START^ 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. COLUMN_SPLIT^ Magic Month No. * | January | 1 | 4 | 4 | March | | April | 0 | 2 | 5 | June | | July | 0 | 3 | 6 | September | | October | 1 | 4 | 6 | December | COLUMN_SPLIT^ Magic Century No.** | 1700 - 1799 | 4 | | 1800 - 1899 | 2 | | 1900 - 1999 | 0 | | 2000 - 2099 | 6 | | 2100 - 2199 | 4 | COLUMN_END ---- !! Example Let's do 29th April, 1951. COLUMN_START^ Add together: | 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 COLUMN_SPLIT^ | Remainder | Day of the Week | | |>> 1 <<| | Sunday | | |>> 2 <<| | Monday | | |>> 3 <<| | Tuesday | | |>> 4 <<| | Wednesday | | |>> 5 <<| | Thursday | | |>> 6 <<| | Friday | | |>> 0 <<| | Saturday | COLUMN_END ---- Notes: * 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 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.