The objective of the number drop game is to try and get a row of numbers in order by selecting certain ones that you want to drop to the end of the line. When you drop more than one number they move to the end while still keeping their relative order and the numbers you didn't drop move to the front while still keeping their relative order. You keep doing that until all the numbers are in order.

Solve these in the fewest moves possible:

1)1 3 5 7 9 2 4 6 8 10
2)10 9 8 7 6 5 4 3 2 1

For ex: 34521

drop 34 = 34521 -> 52134
drop  2 = 52134 -> 51342
drop 34 = 51342 -> 51234
drop  5 = 51234 -> 12345

So have a solution for adjacent drops and a solution for not adjacent drops. 

Only dropping adjacents gives: 3, 4, 5, 6, 7, 8, 9,10 (7 moves) for the first set and gives: 2, 3, 4, 5, 6, 7, 8, 9, 10 (9 moves) for the second set.

As for the other set, I haven't found a better solution than the one supplied: 3,4, 5,6, 7,8, 9,10 (5 moves) but in the second problem,how about a first drop: 10, 8, 6, 4, 2 and proceed like in problem  3,4, 5,6, 7,8 9,10 (6 moves) to give a shorter solution.