1. Design a Turing machine that once started will use no more than a single cell on its tape but will never reach its halt state.
2. Design a Turing machine that places 0s in all the cells to the left of the current cell until it reaches a cell containing an asterisk.
3. Suppose a pattern of 0s and 1s on the tape of a Turing machine is delimited by asterisks at either end. Design a Turing machine that rotates this pattern one cell to the left, assuming that the machine starts with the current cell being the asterisk at the right end of the pattern.