feira treze - What is the maximum number of Friday the 13ths that can occur in a non-leap year? In this case, what day of the week does the tenth day of the year fall on?
feira treze - Since the days of the week repeat every 7 days, the difference between the days of the week is given by the remainder when the number of days that have passed is divided by 7. In the table below,

(a) in the first row, the number of days between the 13th of one month and the 13th of the following month;

(b) in the second row, the remainder obtained when this number is divided by 7;

(c) in the third row, the remainder obtained when dividing by 7 the number of days between the 13th of January and the 13th of the corresponding month; thus, this number is obtained by summing the results obtained in the first row, from January to the corresponding month, and then calculating the remainder of the division by 7.

| J-F | F-M | M-A | A-M | M-J | J-J | J-A | A-S | S-O | O-N | N-D |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 31 | 28 | 31 | 30 | 31 | 30 | 31 | 31 | 30 | 31 | 30 |
| 3 | 0 | 3 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 |
| 3 | 3 | 6 | 1 | 4 | 6 | 2 | 5 | 0 | 3 | 5 |

The equal values in the last row mean that, in those months, the 13th fell on the same day of the week. In particular, the last row tells us that the 13th of February, the 13th of March, and the 13th of November correspond to the same day of the week. Thus, at most, we have three Fridays the 13th.

In the case of three Fridays the 13th in the same year, the 13th of January occurred 3 days before Friday, that is, on a Tuesday, and the 10th of January occurred 3 days before, that is, on a Saturday.

Note: A Friday the 13th occurs only when the first day of the month falls on a Sunday. Thus, another, perhaps simpler, way to solve the problem is to determine the maximum number of times the first day of the month falls on a Sunday in a non-leap year.