Puzzles and logic › Clocks and calendars
Calendars
Solve the first problem 17 problems
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- Shared sale dates in July ●○○○○ 10 ptsA bookstore has a sale on days of the month that are multiples of 5 (such as June 5, June 10, ...). A shoe store has a sale every 6 days. The shoe store has a sale on July 3. How many times in July do the two stores have sales on the same date?
- Working days in a 31-day month ●○○○○ 10 ptsA month of 31 days begins on a Friday. The second and fourth Saturdays of the month and every Sunday are holidays. How many working days are there in the month?
- Non-leap years between 1801 and 1900 ●○○○○ 10 ptsHow many non-leap years are there from 1801 to 1900 inclusive, in the Gregorian calendar?
- Months with five Fridays ●●○○○ 20 ptsOne year, January 1 and April 1 were both on a Thursday. How many months in that year have five Fridays? Justify your answer.
- Maximum months with five Sundays ●●○○○ 20 ptsA month can have at most 5 Sundays. In a year of 12 months, what is the maximum number of months that can have 5 Sundays?
- Maximum leap years in 150 years ●●○○○ 20 ptsIn a calendar system in which leap years occur every four years, with no exceptions, what is the maximum possible number of leap years in a 150-year period?
- Library visits of two friends ●●●○○ 50 ptsXiao Ming goes to the library on the first Wednesday of January, and then again every 4 days, meaning there are 4 days between visits (so the second visit is on a Monday). Xiao Qiang goes to the library on the first Thursday of January, and then again every 3 days, meaning there are 3 days between visits. If in January the two went to the library together only once, on which day of January was this?
- Exactly two friends visiting Daphne ●●●○○ 50 ptsDaphne is visited periodically by her three best friends, Alice, Beatrix and Claire. Alice visits every third day, Beatrix every fourth day, and Claire every fifth day. All three friends visited Daphne yesterday. On how many days of the next 365-day period will exactly two friends visit her?
- Five Sundays in February ●●●○○ 50 ptsApril 16, 2011 was a Saturday. Find all years in the 21st century (2001–2100) in which February has five Sundays.