# What is the maximum amount of amended holidays? (in Brazil)

Every beginning of the year that old doubt arises… how many holidays on weekdays will we have?

This is a complicated question to answer at the regional level, as there are municipal and state holidays and many others that affect specific classes/groups, such as October 28th, which is public servants’ day.

According to Law nº 662, of April 6, 1949, revised by Law nº 10.607, of December 19, 2002, the following days are national holidays:

- January, 1st
- April 21st
- May 1
- September 7th
- November 2nd
- November 15th
- December 25th

We will define that every national holiday that coincides with:

- Tuesday will automatically amend with Monday.
- Thursday will automatically amend with Friday.

Note that the above definition affects the day before the start of the year, and the last day of the year (as it will be before the January 1st holiday of the following year). Thus, to solve our problem, which is the greatest number of holidays amended in a year, we will consider from January 1st to December 31st of that respective year.

Let’s start by assuming that the year is not a leap year, thus, placing the 8 dates (considering the effect of January 1st of the following year in relation to December 31st of the respective year) in relation to the 365 days of the year, we have:

- January 1st: 1
- April 21: 111
- May 1: 121
- September 7th: 250
- November 2nd: 306
- November 15: 319
- December 25th: 359
- January 1 (following year): 366

Now considering the remainder of the integer division by 7, of each of these dates, we have:

- January 1st: 1 mod 7 = 1
- April 21: 111 mod 7 = 6
- May 1: 121 mod 7 = 2
- September 7: 250 mod 7 = 5
- November 2: 306 mod 7 = 5
- November 15: 319 mod 7 = 4
- December 25: 359 mod 7 = 2
- January 1 (following year): 366 mod 7 = 2

These numbers allow us to determine from a stipulated day of the week, which days of the week the other holidays will be. Let’s do an example to illustrate:

- IF January 1: 1 mod 7 = 1 = SUNDAY (0 holidays)
- April 21: 111 mod 7 = 6 = FRIDAY (1 holiday)
- May 1: 121 mod 7 = 2 = MONDAY (1 holiday)
- September 7: 250 mod 7 = 5 = THURSDAY (2 holidays)
- November 2: 306 mod 7 = 5 = THURSDAY (2 holidays)
- November 15: 319 mod 7 = 4 = WEDNESDAY (1 holiday)
- December 25: 359 mod 7 = 2 = MONDAY (1 holiday)
- January 1st (following year): 366 mod 7 = 2 = MONDAY (0 public holidays, as December 31st will be Sunday)

Now we will present the results case by case:

- IF JANUARY 1 IS:
- SUNDAY: 8 days of amended holidays.
- MONDAY: 10 amended public holidays.
- TUESDAY: 5 amended public holidays.
- WEDNESDAY: 6 amended public holidays.
- THURSDAY: 8 amended public holidays.
- FRIDAY: 7 amended public holidays.
- SATURDAY: 6 days of amended holidays.

Now, let’s analyze the situation in which the year is a leap year, thus placing the 8 dates (considering the effect of January 1st of the following year in relation to December 31st of the respective year) in relation to the 366 days of the year and already performing the remainder of integer division by 7, we have:

- January 1st: 1 mod 7 = 1
- April 21: 112 mod 7 = 0
- May 1: 122 mod 7 = 3
- September 7: 251 mod 7 = 6
- November 2: 307 mod 7 = 6

November 15: 320 mod 7 = 5

December 25: 360 mod 7 = 3

January 1 (following year): 367 mod 7 = 3

These numbers allow us to determine from a stipulated day of the week, which days of the week the other holidays will be. We will do it case by case:

- IF JANUARY 1 IS:
- SUNDAY: 9 amended public holidays.
- MONDAY: 4 amended public holidays.
- TUESDAY: 8 amended public holidays.
- WEDNESDAY: 7 amended public holidays.
- THURSDAY: 8 amended public holidays.
- FRIDAY: 7 amended public holidays.
- SATURDAY: 8 days of amended holidays.

Well, finishing the calculations, let’s see what the next year awaits us XD.

January 1, 2023 is a non-leap year and it starts on a Sunday…

That gives us 8 amended holidays… not bad :3 but let’s hope 2029 is coming! Next year we will have our best year for amended holidays, 10.

Cover image credits to Mohamed Hassan by Pixabay