Write the collection of clauses you would get for the following set of tiles $($assume these are

all laid flat and there are no tiles other than the four that are shown$),$ with k $=2.$

The input to the Magnet Tile Building Problem

consists of:

$$ a list of tiles in the structure numbered from $1$ to n$,$ each of which has an identifier from $1$ to r

specifying the shape of the tile;

$$ a set of m ordered pairs $($i$,$ j$)($with i $$ j$)$ which indicates that tile i is connected to tile j;

$$ the number of available colours k$.$