This puzzle challenges you to place a specified number of blocks onto a grid so that rolling/falling balls come out of the grid as predicted. One ball is rolled from left to right along each row of the grid. If it encounters a block, the ball will start to fall (roll downward). If a ball rolling down a column encounters a block, it will roll to the right until it no longer has a block directly under it; with no block under it, the ball will resume its fall.

You are told the number of blocks to be placed. You are also told the number of balls escaping from each row and column. Your task is to place the blocks so that the counts come out right.

Let’s look at an example asking you to place 4 blocks:

The left column in every puzzle can never have a block because the ball rolled from the left would never be able to enter the grid. Put a dot in the middle of each square in the left column to remind you that no block can go there.

The ball falling out of the right column can only occur if a ball falls, hits a block, rolls to the right, and falls again. We know this because we cannot place a block outside the grid to make a ball fall down the right column. Place a dot in each of the bottom two squares of the right column to allow an exit for the ball.

Although it is sometimes possible for a ball to escape the right side of the grid without going directly through the grid in a straight line, this sample grid probably follows the obvious route straight through. Fill the squares on the second and third rows with dots to indicate that no blocks go there.

The grid now has only 5 possible squares for the four blocks.

The ball that drops out of the left column must get deflected by a block in the second column of the bottom row. The ball from the top row must be the ball that falls out of the right column; it will be deflected and fall down the second column. Then it will roll across two blocks before it falls out the right column. The fourth block gets placed in the upper right square. The answer looks like this:

Puzzle 1, Place 3 blocks.

Puzzle 2, Place 3 blocks.

Puzzle 3, Place 6 blocks.

Puzzle 4, Place 13 blocks.

Puzzle 5, Place 5 blocks.

Puzzle 6, Place 15 blocks.