I tried the digits 0,1,4,7 as a candidate generator of all the dates in April i.e. 1 to 30 (in my head, of course) : 1, 1+0!, 4-1, 4, 4+1, 7-1, …7*4+1, 7*4+1+0! and (check whether I err) found out that her date allows to create all the dates of April.

Now - solve the following puzzle:

a. How many dates in a leap year can be considered “a perfect generator” for the month they represent, provided each of the four digits of MM/DD can be used once and any of the operators “+ - * / ^ and ! “ twice at most. Concatenation: only numbers.

b. What dates are the worst generators i.e. create the lowest quantity of dates?

c. What perfect generator has the lowest sum of digits in its MMDD?

d. What would be the answer to a. if a sqrt operator were allowed as well?

Brackets, of course, are allowed.