Five Weekends
Read the puzzle
A clue reads: "This month has five Fridays, five Saturdays and five Sundays." Below it is a row of day tiles: MON, TUE, WED, THU, FRI, SAT, SUN. The question asks: what day of the week is the 1st of this month?
What day of the week is the 1st?
How many days must the month have for 3 days of the week to come 5 times?
Friday
31 days = 4 weeks + 3 days, and those 3 extra days start the month: Friday, Saturday, Sunday.
How to solve it
Step one: work out how long the month must be. Any 28 days hold exactly four of each weekday, because 28 = 4 × 7. A weekday only reaches five when the month has extra days past the 28th. Three weekdays come five times, so there must be 3 extra days, and the month has 28 + 3 = 31 days.
Step two: see which days are the extras. Days 29, 30 and 31 fall on the same weekdays as days 1, 2 and 3, since each is exactly 28 days later. So the weekdays that appear five times are the weekdays of the 1st, 2nd and 3rd.
Step three: put them in order. Those three days are Friday, Saturday and Sunday, in that order, so the 1st is a Friday.
A common wrong answer is Saturday or Sunday, from thinking of the weekend as the start. Another is to try a 30-day month, which gives only two weekdays five times.
Quick check: Fridays fall on the 1st, 8th, 15th, 22nd and 29th, Saturdays on the 2nd, 9th, 16th, 23rd and 30th, and Sundays on the 3rd, 10th, 17th, 24th and 31st: five each.
