Math Olympiad 3

Calendar Problems( Week 27 Evaluation)

1. If there are 4 Mondays within June in a year, which of the following can be the last day of the month?

A	B	C
Sunday	Tuesday	Monday

2. If there are 5 Saturdays within October in a year, which of the following can be the last day of the month?

3. If there are 5 Mondays within December in a year, which of the following can be the 1st day of the month?

4. Below is a calendar of a certain month in a certain year. When you add up all the numbers in a column, you get a column sum. What is the smallest column sum?

5. Below is a calendar of a certain month in a certain year. When you add up all the numbers in a column, you get a column sum. What is the largest column sum?

7. Below is a calendar of a certain month in a certain year. When you add up all the numbers in a column, you get a column sum. What is the largest possible difference between any two column sums?

8. Below is a calendar of a certain month of a certain year. Each cell on the calendar is a 1x1 square. There are 24 possible 2x2 grids (Do not count the title row of the grid). What is the smallest sum of the numbers in a 2x2 grid (If a cell has no number, assume it will be a 0)?

9. Suppose today is Wednesday. What day of the week was it 77 days ago?

10. If the current month were August, which month would it be 92 months from now?