361. Moving Chips. Divide a sheet of paper into 6 squares and place a stack of 15 chips numbered $1,2,3, \ldots, 15$ in square $A$ (see figure), with the numbers going from top to bottom. The puzzle is to move the entire stack to square $F$ in the fewest possible moves. You can move one chip at a time to any square, but a chip with a higher number cannot be placed on a chip with a lower number.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-116.jpg?height=357&width=443&top_left_y=1055&top_left_x=812)

For example, if you place chip 1 in square $B$ and chip 2 in square $C$, you can then place chip 1 on top of chip 2, but not chip 2 on top of chip 1.
361. In 9 moves, form a stack of five chips (from 1 to 5) in square \(B\). In 7 moves, build a stack of four chips (from 6 to 9) in square \(C\). Form a stack of three chips (from 10 to 12) in \(D\) in 5 moves. Place a stack of two chips (13 and 14) in \(E\) in 3 moves. Move one chip (15) to \(F\) in 1 move. Move 13 and 14 to \(F\) in 3 moves, 10 and 12 to \(F\) in 5 moves, from 6 to 9 in 7 moves, and from 1 to 5 in 9 moves. In total, this will take 49 moves.