# Hardcore Lighting - Excalidraw

Each yellow cell is a light that shines in exactly one direction, horizontally, vertically, or diagonally, endlessly, and goes through any block as long as the block is not a wall. Black cells do not symbolize walls.

In each letter, there is a number signifying the number of walls in that letter. All walls are inside a letter. You must place exactly that many walls in that letter, such that there is exactly one way to direct the lights such that the cells occupied by letters and only these cells are unlit (including walls).

There is exactly one correct way to place this many walls, but you won't need this information to solve the puzzle.

Example:

If you want to place just one wall, only the boxed squares are possible solutions, since otherwise the direction of the lights are not unique; for instance, setting R2 C4 to wall enables x to direct to the right as well as to bottom left. The question will not ask you to place one wall only since there are two possible solutions. If you want to place two walls, the only possible way is to place both the boxed squares.

• I am not sure whether the solution is unique, that is, I'm not sure that the way to place the walls to ensure the directioning is unique is unique, but I am sure that there is a solution, that is, there is a way to place the walls to ensure the directioning is unique.
– Sny
Commented Jan 29 at 4:58
• I think that is ok as far as I am aware it is not necessary that grid deduction puzzles have a unique solution path it’s just that the end result has to be unique but there should be a way to completely work out the grid without trial and error though… Have you got path for that???
– PDT
Commented Jan 29 at 5:20
• Ima try to see if there is a path, I think there is, lemme check...
– Sny
Commented Jan 29 at 6:22
• Updated question, initial board was pretty much completely wrong, sadge. Now we should have a unique solution of walls that yields a unique solution of lights, totally deducible.
– Sny
Commented Jan 29 at 7:25
• I'm not sure how the example works here. What's X in the example? Why not just place one wall to the right most of X? Commented Jan 29 at 7:59

Here is the solution

The grey tiles are walls, the yellow are the lighted tiles, the red is the tile that cannot be shaded in order for a unique solution. N E S W denote the North, East, South and West and 1, 3, 7, 9, denote NW, NE, SW, SE.

Or

There are a lot of deductions here so I would rather give some tools and tips to help future solvers:

1)

Start with the sides and work towards the center as it will lead to straightforward and/or essential deductions to help proceed in solving the grid:

Top and bottom E lamps are obvious since that is the only direction that satisfy the fact that the E letter has zero walls and right away we have figured out two walls of the X. The middle E lamp has the only solution as only with that lamp and that directionality the R3C7 tile can be lit! So with these straightforward deductions we have already worked out not only 3 lamps but (all) 3 walls of a letter!

You can see here in the bottom row the center tile can only be lit by the S Lamp being a south pointing one and the 7 and 9 lamps are needed therefore to light the squares that are adjacent to the bottom middle lit square and be SW and SE facing respectively. As for the top half of the letter the S lamp cannot light the tiles to the left or right of it since the remainder would force two walls to be made but the tile below it cannot be lit by either of the N tiles either as that would necessitate again 2 walls to be made… so the tiles needs to be lit by the S lamp and so it needs to be in a South pointing direction and the adjacent sides of the S lamp need therefore then to be lit by the two N lamps pointing northwards…

Spot obvious places that can only be lit by a certain Lamp in order to determine its direction. Green here highlights such a square and the 9 is a deduced square as a result of the recognition:

Spotting these often will solve the issue when there are competing Lamps for a certain lighted tile. And by deducing such lamps, it will open other areas that can only be lit by a certain Lamp!

Be mindful if such a light hits a letter. If this happens one has to shade them in as a wall. And be aware that the letters only has a certain amount of walls each. This (apart from preventing a wrong solution) will also help when there are competing light sources for certain tiles.

Filling out the grid in terms of the areas lit up by the lamps after deducing them is helpful too (as shown below by the yellow tiles) to keep track of unlit tiles and places where the light reaches:

Here are some tricky spots and their solutions:

1. The right side of the I

Assuming you have been progressing from the sides to the center… as you can see the S lamp needs to be South pointing. Otherwise the two W lamps have to cover the green tiles and so there will always at least be two tiles unlit. For example as shown in the blue…

So the S lamp has to be south facing… and then we have the green tile that is needing a lamp to cover it and it can’t be the w lamp since then there would be too many walls for the letter I and so it has to the be the 7 lamp pointing in a SW direction.

The green then needs to be covered by the N lamp being North pointing which leaves the remaining tiles having to be covered by the W lamps facing in the Western direction.

1. Finding the tile in the D that cannot be shaded:

We know that if we find the unshaded tile that forces a unique solution we have got the solution for that tile!

(The 3 tile and N tile has already been deduced using tool 2 above). What we are looking for, is something that prevents the E lamp from being a south pointing one since it means that the top W lamp must be a Western facing one to light the top green tile leaving only the bottom W lamp being able to light the bottom Green tile. The blue tile therefore then can only be lit by the E lamp facing East which then leaves the 1 Lamp being the only lamp able to light the pink tile facing in a NW direction!! So the red tile being non wall is the tile we are looking for since it forces this sequence which allows the grid to be completed in only one way! And the rest of the tiles in the D are to be shaded as a wall therefore since there has to be 13 walls for the letter and has only 14 unshaded tiles to compose it.

• I would personally give this puzzle a very solid 9/10 very enjoyable indeed. You should make more of these kind of grid deductions. The SNY puzzle yesterday would have been more fun with this kind of format!!
– PDT
Commented Jan 29 at 11:03
• Best puzzle would go to the chess puzzle I thought that one was brilliant!
– PDT
Commented Jan 29 at 11:05