In high school, one of my favourite contests is the CNML (Canadian National Mathematics League). The contest is still in existence now. Out of curiosity, I bought online access to all the contests recently. The questions are generally not too difficult. Each year consists of 6 contests of 6 questions each to be done in 30 minutes. I sometimes kill time by pretending to write these contests as though I was a student. I also like the caricatures that often accompany the questions which add life to the contest itself. The following question stood out because of its relevance to daily life.
Problem: What is the minimum and maximum number of Friday the 13th in a given calendar year?
Solving this problem is a matter of noticing that the day of the week the 13th of each month falls in a calendar year is completely determined by whether it is a leap year or not and what day of the week January 1st falls in. Hence there are 2 X 7 = 14 cases. Going through the different cases shows that there is a minimum of 1 and a maximum of 3 Friday the 13th each year. Thus in every year, you are guaranteed at least one Friday the 13th.
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