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2 A perfect number that is equal to the sum of its proper factors. Find the

perfect numbers from 2 to 20.

Factors of 28 : 1, 2, 4, 7, 14, 28

1 + 2 + 4 + 7 + 14=28

28 is a perfect number.

3 There are one hundred windows and one hundred cleaners in a castle. The

cleaners clean the windows everyday and they will follow the below methods
to open closed windows, close opened windows to find the windows that are
finally left open in the afternoon.

1. First cleaner opens all windows.
2. Second cleaner closes all windows that are multiples of 2.
3. Third cleaner closes all opened windows and opens all closed
windows that are multiples of 3.
4. Forth cleaner closes all opened windows and opens all closed
windows that are multiples of 4.
5. All the remaining cleaners either close all opened windows
and open all closed windows based on the multiples their order
of cleaning.

3. Factors 37