When you move the top block over so that it just balances, its center of gravity, or balance point, rests over the edge of the block below. Each time you move a block, you are finding the center of gravity of a new stack of blocks—the block you move plus the blocks above it. The edge of each block acts as a fulcrum supporting all the blocks above it.
By considering the positions of the centers of gravity of the blocks as the stack is built, it can be shown that the first block will be moved 1/2 of a block length along the second block, the top two blocks will be moved 1/4 of a block length along the third block, the top three blocks will be moved 1/6 of a block length along the fourth block, the top four blocks will be moved 1/8 of a block length along the fifth block, and so on. Do you see the pattern?
How far will the nth block be moved along the block below it? The answer is: 1/2n of a block length along the n + 1 block. Unavoidable experimental error due to factors such as nonuniformity of blocks and inexact location of balance points will lead to actual values that are not quite in agreement with theory but that are still probably close enough to make the point.