Number of Turing machines Do you have any idea about this question? I do not know what it asks.
-What is the number of Turing machines with with the state set  $\{Q-\text{start}, Q2, Q3, Q4, Q5, Q6, Q-\text{accept}, Q-\text{reject}\}$, input alphabet $\{0,1\}$ and tape alphabet $\{0,1,\text{x},\text{U}\}$ where $\text{U}$ is the blank symbol? The start, accept and reject states are the ones with the appropriate names. Show your work.
 A: Assuming the quadruple formalization of Turing-machines, every transition is of the form $<Q_i, S_j, A_{ij}, Q_{ij}>$: 'If you arer in state $Q_i$ and read symbol $S_j$, perform action $A_{ij}$ (which is either to move left or right or print a symbol), and go to new state $Q_{ij}$:
you have $6$ choices for $Q_i$ (the $Q_{Accept}$ and $Q_{Reject}$ do not have any outgoing transitions)
You have $4$ choices for the symbol you are reading
You have $6$ choices for the action: move left, move right, or print any of the $4$ symbols
You have $8$ choices for the new state
So: for each of the $6\cdot 4 = 24$ entries in the transition-table, you have $6\cdot8=48$ possibilities, giving you $48^{24}$ possible Turing-machines using the quadruple formalization.
Assuming the quintuple formalization of Turing-machines, every transition is of the form $<Q_i, S_j, S_{ij}, A_{ij}, Q_{ij}>$: 'If you are in state $Q_i$ and read symbol $S_j$, print out symbol $S_{ij}$, perform action $A_{ij}$ (move left or right), and go to new state $Q_{ij}$:
you have $6$ choices for $Q_i$ (the $Q_{Accept}$ and $Q_{Reject}$ do not have any outgoing transitions)
You have $4$ choices for the symbols you are reading
You have $4$ choices for the symbol you are writing
You have $2$ choices for the action: move left or move right 
You have $8$ choices for the new state
So: for each of the $6\cdot 4 = 24$ entries in the transition-table, you have $4\cdot2\cdot8=64$ possibilities, giving you $64^{24}$ possible Turing-machines using the quintuple formalization.
