The reason calendars can't be reused is because the day of the week of a date changes. Suppose that the first day of January in 2009 is a Thursday. Then 365 days later, in 2010, it will be first of January on a Friday, because 364 is a multiple of 7 and so the day of the week increases by 365-364=1.7. If a year has 364 days, then the same calendar could be used every year by only changing the year. A "regular" year has 365 days and a leap year has 366 days. The year 2000 has a leap year and leap years occur every 4 years between the years 2000 and 2100. Claudia has calendar for 2009. What will be the next year that she can use this calendar by merely changing the year?

If you get another first of January on a Thursday, and it isn't a leap year that year, then the calendar can be reused.

2/3 of 6 =4 so there must be at least 4 Ts. There is no easier way to handle this than adding up the numbers of possibilities with 4, 5 and 6 Ts.8. A 6-question True-False test has True as the correct answer for at least 2/3 of the questions. How many different true/False answer patterns are possible on an answer key for this test?