Every Sunday, and the second and fourth Saturday, of a month are holidays. If…

Concept

The number of working days in a month equals the total number of days minus the number of holiday dates. When holidays are defined by weekday (e.g., "every Sunday", "the 2nd and 4th Saturday"), the key step is mapping dates to weekdays: since the weekday pattern repeats every 7 days, once the weekday of date 1 is known, every other date's weekday follows by adding or subtracting multiples of 7.

Working (step by step)

1. The month begins on a Friday, so date 1 = Friday, date 2 = Saturday, date 3 = Sunday, and the weekly pattern repeats from there.

2. Since the pattern repeats every 7 days, every Saturday falls on dates 2, 9, 16, 23, and 30, and every Sunday falls on dates 3, 10, 17, 24, and 31.

3. All 5 Sundays (dates 3, 10, 17, 24, 31) are holidays, since the rule applies to every Sunday.

4. Of the 5 Saturdays, only the 2nd Saturday (date 9) and the 4th Saturday (date 23) are holidays under the stated rule; the 1st, 3rd, and 5th Saturdays (dates 2, 16, 30) remain working days.

5. Total holiday dates = 5 Sundays + 2 designated Saturdays = 7.

6. Working days = total days − holiday dates = 31 − 7 = 24.

Cross-check

Splitting the month's 31 dates by weekday independently confirms this: 31 = 4×7 + 3, so with date 1 on a Friday, the first three weekdays of the cycle (Friday, Saturday, Sunday) each occur 5 times, while Monday, Tuesday, Wednesday, and Thursday each occur only 4 times (5+5+5+4+4+4+4 = 31). This confirms exactly 5 Saturdays and 5 Sundays in the month, matching the count used above.

Answer

The month has 24 working days.