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!_ To Find out the Day of the Week of any Day _

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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.

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Magic Month No. *

| January | 1 | 4 | 4 | March |

| April | 0 | 2 | 5 | June |

| July | 0 | 3 | 6 | September |

| October | 1 | 4 | 6 | December |

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Magic Century No.**

| 1700 - 1799 | 4 |

| 1800 - 1899 | 2 |

| 1900 - 1999 | 0 |

| 2000 - 2099 | 6 |

| 2100 - 2199 | 4 |

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!! Example

Let's do 29th April, 1951.

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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

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| Remainder | Day of the Week |

| |>> 1 <<| | Sunday |

| |>> 2 <<| | Monday |

| |>> 3 <<| | Tuesday |

| |>> 4 <<| | Wednesday |

| |>> 5 <<| | Thursday |

| |>> 6 <<| | Friday |

| |>> 0 <<| | Saturday |

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Notes:

* 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.

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This is one of the many Enrichment tasks on this site.