I'm guessing that there's more information missing from
this question than is given ... quite an accomplishment.
It's as if I were to ask you: "I live in Chicago, work as an
engineer, and my car is blue. How old am I ? Explain how
you found your answer."
We need to know something about how much a discount
ticket costs, and/or how much a regular-price ticket costs,
and/or how much the theater took in at the box office last
Saturday.
Working with all the information given in the question, the
least possible number of showings after 4:00 PM could have
been zero, if the operators shut the doors at 4:00 PM and
went home.
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After reading the question again, more carefully this time,
I'll also need to know how many theaters there are in that
movieplex, and if Saturday's box-office take refers to the
whole movieplex, or to only one theater.
