Prove that if L is recognized by a Turing machine with a two-way infinite tape, it can be recognized by a Turing machine with a one-way infinite tape. Suppose a lottery is based on correctly...

Prove that if L is recognized by a Turing machine with a two-way infinite tape, it can be recognized by a Turing machine with a one-way infinite tape. Suppose a lottery is based on correctly picking four integer values, each in the range from 1 to 50. Moreover, suppose that the jackpot grows so large that it becomes profitable to buy a separate lottery ticket for each possible combination. If it takes one second to buy a single ticket, how long would it take to buy one ticket for each combination? How would the time requirement change if the lottery required picking five numbers instead of four? What does this problem have to do with the material from this chapter?