Egyptian Fractions

An egyptian fraction has a numerator equal to 1, and its denominator is a positive integer.
  1. Find the maximum number of different egyptian fractions such that their sum is equal to 1, and their denominators are equal to 10 or less.
  2. Same question for all the denominators < or = 25.
  3. Same question for all the denominators < or = 50.
  4. Same question for all the denominators < or = 100.
  5. How to proceed for all the denominators < or = any given integer number N >100?

Source: Philippe Fondanaiche, citing Tangente n 65/66 L. Pianaro, with his original extensions.


Solution
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