There are $n$ adults in town A and they all need to go to town $B.$ There is only a single motorbike

available which is owned by two boys. The motorbike can carry exactly one adult or one or two

boys at a time. Show how all adults can be moved from town A to town B while, at the end,

leaving the motorbike with the two boys in town A$.$

Show the correctness of your algorithm by using mathematical induction and analyze the number

of trips needed. $($Hint: Use decrease and conquer to reduce the problem size.$)$