What was the day of the week on 28th may, 2006?

General
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what was the day of the week on 28th may, 2006?

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What was the day of the week on 28th May, 2006?

Answer: To determine the day of the week for 28th May 2006, we can use a method known as Zeller’s Congruence, a mathematical algorithm devised to calculate the day of the week for any date.

Calculating Using Zeller’s Congruence

Zeller’s Congruence formula is:

h = \left(q + \left\lfloor \frac{{13(m + 1)}}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor - 2J \right) \mod 7

where:

  • ( h ) is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, …, 6 = Friday).
  • ( q ) is the day of the month.
  • ( m ) is the month (3 = March, 4 = April, …, 12 = December), January and February are considered months 13 and 14 of the previous year.
  • ( K ) is the year of the century (year \mod 100).
  • ( J ) is the zero-based century (year / 100).

For the date 28th May 2006:

  • The day ( q = 28 ).
  • The month ( m = 5 ) (since May is treated as May and is the 5th month).
  • The year is 2006.
    • ( K = 2006 \mod 100 = 6 ).
    • ( J = \left\lfloor \frac{2006}{100} \right\rfloor = 20 ).

Now, substituting into Zeller’s formula:

h = \left(28 + \left\lfloor \frac{{13(5 + 1)}}{5} \right\rfloor + 6 + \left\lfloor \frac{6}{4} \right\rfloor + \left\lfloor \frac{20}{4} \right\rfloor - 2 \times 20 \right) \mod 7
  • Calculate: ( \left\lfloor \frac{{13 \times 6}}{5} \right\rfloor = \left\lfloor \frac{78}{5} \right\rfloor = 15 )
  • Calculate: ( \left\lfloor \frac{6}{4} \right\rfloor = 1 )
  • Calculate: ( \left\lfloor \frac{20}{4} \right\rfloor = 5 )

Substituting these values back,

h = (28 + 15 + 6 + 1 + 5 - 40) \mod 7
  • Solve: ( 55 - 40 = 15 )
  • ( 15 \mod 7 = 1 )

Since ( h = 1 ), the day of the week is Sunday.

Therefore, 28th May 2006 was a Sunday.

Key Points to Remember

  1. Zeller’s Congruence helps determine the day of the week for any given date with a formula.
  2. Adjust months for January and February by treating them as 13th and 14th months of the previous year.
  3. Use integer division (floor) to calculate parts of the formula.

This calculation method is reliable for historical day-of-week determination, showing that complex mathematical algorithms can solve everyday questions efficiently.

Remember, 28th May 2006 was a Sunday.

If you need more help with calendar calculations or any similar concepts, feel free to ask! Keep practicing, and soon you’ll find these computations much easier. @anonymous7