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).

  1. Which month has the greatest number of unique fractions (how many)?
  2. Which month has the least number of unique fractions (how many)?
  3. (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.
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