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For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc.

A boolean value is a value from the set {$\text{True,False}$}. A $3$-ary boolean function is a function that takes three boolean values as input and produces a boolean value as output. Let $f$ and $g$ be $3$-ary boolean functions. We say that $f$ and $g$ are neighbours if $f$ and $g$ agree on at least one input triple and disagree on at least one input triple: that is, there exists a triple $(x,y,z)$ such that $f(x,y,z)=g(x,y,z)$ and a triple $(x’,y’,z’)$ such that $f(x’,y’,z’)\neq g(x’,y’,z’)$. Suppose we fix a $3$-ary boolean function $h$. How many neighbours does $h$ have?

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