Binary function from {0,1}^n
Source: Miklós Schweitzer 2018 P7
November 10, 2018
functioncollege contests
Problem Statement
Describe all functions which satisfy the equation
\begin{align*}
& f(f(a_{11},a_{12},\dotsc ,a_{1n}),f(a_{21},a_{22},\dotsc ,a_{2n}),\dotsc ,f(a_{n1},a_{n2},\dotsc ,a_{nn}))\\
& = f(f(a_{11},a_{21},\dotsc ,a_{n1}),f(a_{12},a_{22},\dotsc ,a_{n2}),\dotsc ,f(a_{1n},a_{2n},\dotsc ,a_{nn}))\end{align*}
for arbitrary where