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Ken's Puzzle of the Week

Calendar Fractions

Write each date on a calendar as a fraction MM/DD. Every month has some
fractions which are equivalent in other months. For example, January
2 (1/2) is equivalent to February 4 (2/4) and September 18 (9/18).

- Which month has the greatest number of unique fractions (how many)?
- Which month has the least number of unique fractions (how many)?
- (Advanced) How many different fractions exist in 2008? You may
count the first instance of an equivalent fraction (count March 5, but not
September 15.)

Source: Original.

Solution

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