# Must be a popular lecturer

Number Theory Level 5

Suppose a lecture hall has a rectangular array of chairs with $$r$$ rows and $$c$$ columns. Suppose further that there are precisely $$19$$ girls seated in each row and precisely $$15$$ boys seated in each column.

If exactly $$14$$ chairs are empty then find the minimum possible value of $$r \times c.$$

Details and Assumptions:

• A maximum of one person per chair is allowed.
###### Image Credit: Wikimedia Hobiecat93
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