Question 6
Eighteen boys and $23$ girls plant trees. Each individual plants one. An all-boy group $n$ plants $n + \operatorname{floor} \left(\frac{n + 1}{4}\right)$; an all-girl group $k$ plants $k + \operatorname{floor} \left(\frac{k + 1}{6}\right)$; a mixed group $p , q \gt 0$ plants $p + q + \operatorname{floor} \left(\frac{p + q + 2}{5}\right)$. Find the maximum by combining group plans. For example $\operatorname{floor} \left(\frac{5}{3}\right) = 1 , \operatorname{floor} \left(\frac{10}{5}\right) = 2$.