On which day of the week did 28 May 2006 fall?

Concept

A weekday repeats every seven days, so calendar calculations use remainders modulo 7. In the Doomsday method, every year has one reference weekday on which fixed dates fall.

For a year in the 2000s, add the last two digits of the year, their quotient on division by 4, and the century anchor Tuesday; reduce the sum modulo 7. In a common year, 9 May is a doomsday date.

Application

1. For 2006, the last two digits give 6, and ⌊6 ÷ 4⌋ = 1.

2. Using weekday indices Sunday = 0, Monday = 1, Tuesday = 2, and so on, the 2000s century anchor is Tuesday, with index 2.

3. The doomsday index is (6 + 1 + 2) mod 7 = 9 mod 7 = 2. Thus, the doomsday for 2006 is Tuesday.

4. Because 2006 is not divisible by 4, it is a common year; therefore, 9 May 2006 was Tuesday.

5. The date 28 May is 19 days after 9 May, and 19 mod 7 = 5. Moving five weekday steps from Tuesday gives Sunday.

Cross-check

Zeller’s congruence gives h = [28 + ⌊13 × 6 ÷ 5⌋ + 6 + ⌊6 ÷ 4⌋ + ⌊20 ÷ 4⌋ + 5 × 20] mod 7 = 155 mod 7 = 1. In Zeller’s indexing, 1 denotes Sunday, confirming the result.

Therefore, 28 May 2006 fell on Sunday.