Question 5
In an $8\times8$ grid, $n$ disks, numbered 1 to $n$ are stacked, with random order, in a pile in the bottom left corner. The disks can be moved one at a time to a neighbouring cell either to the right or top. The aim to move all the disks to the cell at the top right corner and stack them in the order $1,2,\ldots,n$ from the bottom. Each cell, except the bottom left and top right cell, can have at most one disk at any given time. Find the largest value of $n$ so that the aim can be achieved.