>**Puzzle 208.** Suppose you some slices of bread, some slices of cheese and some slices of ham. You are trying to make sandwiches. You can make a cheese sandwich with two slices of bread and one slice of cheese. You can make a ham sandwich with two slices of bread and one slice of ham. There is a feasibility relation \$$\Theta : \mathbb{N} \times \mathbb{N} \nrightarrow \mathbb{N} \times \mathbb{N} \times \mathbb{N} \$$ where \$$\Theta(m,n,i,j,k) = \text{true}\$$ if you can make \$$m\$$ cheese sandwiches and \$$n\$$ ham sandwiches from \$$i\$$ slices of bread, \$$j\$$ slices of cheese and \$$k\$$ slices of ham.

$\Theta(m,n,i,j,k) = \begin{cases} \texttt{true} & \mbox{if } m \leq j \mbox{ and } n \leq k \mbox{ and } m+n \leq 4i \\\\ \texttt{false} & \mbox{otherwise.} \end{cases}$