Say "Herru" to Spatial Golf

Have a try with this 3D Herugolf puzzle!

1. Move (hit) all circles (balls) one or more times, and bring them to a cell with a red H (hole). Each ball must end up in a different hole.

2. Show the movement of a ball by an arrow, with the tip of the arrow in the cell where it stops. The arrow cannot cross other balls, holes, or arrows.

3. When it is first hit, a ball travels across as many cells as the number inside it, in a straight line, in any axis (X, Y, and Z). No diagonals and no changing direction partway through a move.

4. Each subsequent shot follows the same rules but crosses 1 cell fewer than the previous shot (e.g. a ball numbered ‘3’ crosses 3 cells on its first shot, 2 on its second, and 1 on its third). The direction of travel may (but doesn’t have to) change after (not during) a shot. When the next shot length becomes 0, or the ball stops at a hole, the ball cannot move any further.

5. A ball cannot leave the grid (“out of bounds”) and cannot stop at the end of a shot in a water hazard or sand trap (brown cells), although it may pass through them if the shot ends on the grass (green cells).

This seems to work (couldn't make arrows, so tried colors instead):

Some notes solving it:

1. First I marked the paths of the 1's as each only had one possible solution.

2. Then I did the 3's which also only had one solution each, except for the 3 at top left which could end at either of two holes in the 3rd layer or one hole in the 4th layer.

3. I then did the 2's starting at the top layer. At this point they only had one solution each. As did the 2's in the second layer. And in the third layer. Some fiddling was needed in the fourth layer, then it was done.

• nice! Could you also explain your logic deduction? Nov 17, 2019 at 3:59