Answer:
15
In general, it takes 2n-1 moves to move n cheeses.
Here's why:
To move one cheese, just move it. That's 21-1=1 move.
To move n cheeses, follow these three major procedures:
A: Move the n-1 cheeses above the nth cheese to the
"stepping stool".
B: Move the nth cheese to a new stool.
C: Move the n-1 cheeses to the new stool.
Procedure A takes 2n-1-1 moves. Procedure B takes 1
move. And procedure C takes 2n-1-1 moves. If you
add up these moves, you will see that
2n-1-1 + 1 + 2n-1-1
= 2n-1
Examples
To move 2 cheeses, it takes 3 moves -- move the small cheese, then move
the second cheese, then move the small cheese.
To move 3 cheeses, it takes 7 moves -- move the two small cheeses (3
moves), then move the third cheese (1 move), then move the two small
cheeses on top of the third cheese (3 moves).
To move 4 cheeses, it takes 15 moves -- move the three small cheeses (7
moves), then move the fourth cheese (1 move), then move the three small
cheeses on top of the fourth cheese (7 moves).
