A cross is the figure composed of $6$ unit squares shown below (and any figure made of it by rotation).
Find the greatest number of crosses that can be cut from a $6 \times 11$ divided sheet of paper into unit squares (in such a way that each cross consists of six such squares).
The answer is 8. Out of the six tiles call the intersection of the column and row $C$. Note that $C$ can only be placed such that you leave a one tile gap from the boundary. There are 30 such boundary tiles of which with one cross you can cover at most two. Thus $\left\lfloor\frac{6 \times 11-\frac{30}{2}}{6}\right\rfloor=8$.
