First Monday of Any Month to a Playing Card

The next step in associating every week in a year with a unique playing card is mentally calculating the first Monday of any month. Our cards will always denote Mondays, for a reason we’ll get to in a minute.

Use the century 1900 because its century number is 0 and we can ignore it, except for Jan and Feb, which we must pretend belong to 1899. The year 1899 is 6 = 2 (for 1800) + 1 (99 mod 7) + 3 ((99 / 4) mod 7).

For this calculation, think of Monday as a 2 or 9. To find the day of the month for the first Monday, just subtract the month number from 2 or 9. Jan 1899 is 1 = 2 (Jan) + 6 (1899) = 8 = 1, so the first Monday in Jan 1900 is 1 Jan. Cool! That’s why we’re going to reckon all our cards from Monday instead of from Sunday or Saturday.

Feb 1900 = Feb 1899 (pretend) = 4 = 5 (Feb) + 6 (1899) = 11 = 4. Subtract from 9. First Monday in Feb 1900 is 5 Feb.

Now it gets much easier for Mar through Dec because we don’t need to carry around the 6 for the pretend century.

First Monday in Jan is 1 Jan
First Monday in Feb is 5 Feb
First Monday in Mar is 9 – 4 (Mar) = 5 Mar
First Monday in Apr is 2 – 0 = 2 Apr
First Monday in May is 9 – 2 = 7 May
First Monday in Jun is 9 – 5 = 4 Jun
First Monday in Jul is 2 – 0 = 2 Jul
First Monday in Aug is 9 – 3 = 6 Aug
First Monday in Sep is 9 – 6 = 3 Sep
First Monday in Oct is 2 – 1 = 1 Oct
First Monday in Nov is 9 – 4 = 5 Nov
First Monday in Dec is 9 – 6 = 3 Dec

Now, starting with Jan and Spade A, count off the number of weeks in the months, which follow the amazing pattern 544/544/544/544. Count off cards in Black-Red-suit order (Spades, Hearts, Clubs, Diamonds) We get

First Monday in Jan is 1 Jan = Spade Ace
First Monday in Feb is 5 Feb = Spade 6
First Monday in Mar is 5 Mar = Spade 10
First Monday in Apr is 2 Apr = Heart Ace
First Monday in May is 7 May = Heart 6
First Monday in Jun is 4 Jun = Heart 10
First Monday in Jul is 2 Jul = Club Ace
First Monday in Aug is 6 Aug = Club 6
First Monday in Sep is 3 Sep = Club 10
First Monday in Oct is 1 Oct = Diamond Ace
First Monday in Nov is 5 Nov = Diamond 6
First Monday in Dec is 3 Dec = Diamond 10

Is that cool, or what?

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~ by rebcabin on July 3, 2015.

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