B$4$ Amend your code to keep track of the total number of moves in the game, by writing a function PlayHanoi$2($pos$,$ a $,$ b$,$ c$,$ n$,$ j$)$ which has an additional input $j($which will be zero on the initial input$)$ to serve as a move$-$counter, and which outputs suitably modified $($pos$,$ j$).$ Define a function WholeGame$2($n$)$ which runs PlayHanoi$2$ on a suitable starting configuration.

This might be tricky depending on how you coded B$3$: the danger is that the counting variable $j$ will assume different values in different subroutines. Make sure you keep careful track of the current game position and number of moves throughout your function.