Suppose Alice has a piece of hardware that does $3$DES but she needs to talk to Bob, whose implementation can only do DES. How can Alice use her $3$DES hardware to communicate with Bob? How many possible variants of $3$DES are there $($where there is a choice of E or D for each key$)?$

Would all of them work as an encryption mechanism, if Alice uses $3$ keys?

How many of these variants would allow Alice to use the trick in first problem to communicate with a Bob that can only do DES?