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Doomsday rule
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===Example 1 (1985)=== Suppose we want to know the day of the week of September 18, 1985. We begin with the century's anchor day, Wednesday. To this, add {{math|''a''}}, {{math|''b''}}, and {{math|''c''}} above: *{{math|''a''}} is the floor of {{math|{{sfrac|85|12}}}}, which is 7. *{{math|''b''}} is {{math|85 mod 12}}, which is {{math|1}}. *{{math|''c''}} is the floor of {{math|{{sfrac|''b''|4}}}}, which is 0. This yields {{math|''a'' + ''b'' + ''c'' {{=}} 8}}. Counting 8 days from Wednesday, we reach Thursday, which is the doomsday in 1985. (Using numbers: 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, i.e. one day less than two weeks. Hence, the 18th was a Wednesday (the day preceding Thursday). (Using numbers: In modulo 7 arithmetic, 13 is congruent to 6 or, more succinctly, β1. Thus, we take one away from the doomsday, Thursday, to find that September 18, 1985, was a Wednesday.)
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