Pinball Wizard

Normal sudoku rules apply.

Digits in cages sum to the clue in the top left corner.

Three pinballs start at the top of the grid, trace a path around the table, and finish at the bottom of the grid. The number of cells visited by each path (including start and end cells) is given in the associated end cell.

Each ball may move sideways or downwards (diagonally or straight) any number of times, but may move upwards (diagonally or straight) at most TWICE, on its journey. Balls may not enter any cell more than once. Balls may not enter a grey shaded cell or a 'bumper' cell (given digit). Each ball must visit each of the three 'target' cages (shaded yellow) in order (ABC) along the way, passing through the indicated cells.

No path shares any cells, and while they may cross other paths diagonally, no path crosses itself.

Box borders divide the blue path into segments with the same sum.

Adjacent digits along the green path must differ by at least 5.