*Kool*if the sum of all its elements equals their product.

For example, {2, 2, 2, 1, 1} is a *Kool* set.

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a) Show that there exists a *Kool* set of *n* numbers for all *n*>1

b) Find all *Kool* sets with sums of 100

c) Find all *Kool* sets with 100 members.