 To show that the house can be built to order, we need to show that each builder separately can carry out his or her appointed task, regardless of what the other builders do. So we imagine each builder as player \(\exists\) in a game where all the other players are lumped together as \(\forall\), and we aim to prove that \(\exists\) has a winning strategy for this game. When we have proved this for each builder separately, we can imagine them going to work, each with their own winning strategy. They all win their respective games and the result is one beautiful house.