>**Puzzle 206.** Suppose you are trying to feed hungry children with the loaves of bread you bought in the previous puzzle, and you can feed at most three children with each loaf of bread. Describe this using a feasibility relation \\(\Phi : \mathbb{N} \nrightarrow \lbrace 0,1,2\rbrace \\). Here \\(\mathbb{N}\\) is the set of natural numbers \\( \lbrace 0,1,2,3,\dots \rbrace \\) with its usual ordering.

\[

\Psi(x, y) =

\begin{cases}

\texttt{true} & \mbox{if } (x \leq 0 \mbox{ and } y = 0) \mbox{ or } (x \leq 3 \mbox{ and } y = 1) \mbox{ or } (x \leq 6 \mbox{ and } y = 2) \\\\

\texttt{false} & \mbox{otherwise.}

\end{cases}

\]

\[

\Psi(x, y) =

\begin{cases}

\texttt{true} & \mbox{if } (x \leq 0 \mbox{ and } y = 0) \mbox{ or } (x \leq 3 \mbox{ and } y = 1) \mbox{ or } (x \leq 6 \mbox{ and } y = 2) \\\\

\texttt{false} & \mbox{otherwise.}

\end{cases}

\]