Cipher text on an ancient wall

Question

The following text was found written on the wall of an ancient tomb:

$\text{DXFDMKEPU}$

Can you decipher what it means?

Nearby the wall, this piece of parchment was found. Perhaps it is a clue for deciphering the word?

The following instructions were found (seemingly referring only to the grid on the left):

Shade 22 squares in the grid such that:

• No number appears in a row or column more than once (shade boxes to remove duplicates).
• No shaded square is adjacent to another shaded square vertically or horizontally.
• When completed, all un-shaded squares create a single continuous area. (Example)

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Hint 1:

1 2 3 4 5 6 7 8 9
D X F D M K E P U

Hint 2:

New information reveals that the parchment actually contains notes on how to encode the word written on the wall. I'm sure by working backwards, you can use this note to decipher the text as well.

Answer 1

^{This answer resolves the final message concealed in the puzzle. The initial grid-deduction puzzle was solved by @BeastlyGerbil - go upvote their answer for finding that part of the solution.}

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Final answer:

The one-word message hidden in the puzzle is meant as feedback from the OP on your efforts in solving it. The OP says:

EXCELLENT

How to get there...

First, make note of @BeastlyGerbil's solution to the initial puzzle:

^{For full details on how to solve this step of the puzzle, see BG's answer (and consider leaving a +1).}

For our intents and purposes, what is especially crucial to the final answer is overlaying the shaded squares from the left-hand grid onto the right-hand grid.

Note from the second hint that:

the solved puzzle describes how to encode (not decode) the original ciphertext, 'DXFDMKEPU'.

So how to do this? First, note down the shaded 'L' and 'R' sequences in each row (numbered 1-9) of the solved puzzle, gaining us:
LRL / RL / RRR / L / RLR / LLR / LR / RRLR / R

Note then that these letter groups show to us how to create the 9-letter ciphertext. If we treat the alphabet as a letter-line, arranged from A to Z in order, these 'L' and 'R' characters represent LEFT and RIGHT movements through the alphabet in order to reach the letters in 'DXFDMKEPU'.

Immediately, notice that this means one 'L' will cancel out one 'R', and vice versa, since this purely returns us to the spot from which we came. Because of this we can simplify our letter groups to:
L / (no movement) / RRR / L / R / L / (no movement) / RR / R

To find the original letters:

simply take the ciphertext and substitute each 'L' in the instructions for an 'R' and each 'R' for an 'L', their reverse operations. This means we need to apply the following shifts to the letters in the ciphertext:
R / (no movement) / LLL / R / L / R / (no movement) / LL / L

Starting from 'DXFDMKEPU' we then get:
D --> E (R)
X --> X (no movement)
F --> C (LLL)
D --> E (R)
M --> L (L)
K --> L (R)
E --> E (no movement)
P --> N (LL)
U --> T (L)

i.e. it spells out 'EXCELLENT'...

Answer 2

The final answer is

EXCELLENT

To see how this is found, check out Stiv’s Answer where he realises what to do with the grid once solved!

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Partial answer: Solved grid

And if it correlates to the second grid then:

And some notes:

- The encrypted word is 9 letters, so probably corresponds to rows/columns
- The Ls and Rs are obviously standing for left and right, so perhaps this is a caesar shift on each letter
- Perhps the row number is how much we shift the letter? Just not sure how the word correlates to the grid

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Step by step for the grid:

1:

The fact there are three 2s in a row means this is the only way for one 2 to be left in the column using the adjacency rule. The 2s then rule out the adjacent 7s from being greyed out, so it must be the other 2

2:

The three ones down the left can now only be greyed out as so. This aslo greys out a one on the right.

3:

The 5 at the bottom means the 5 top left must be greyed out. Now if we try greying out the 4s and 5s at the top like so we get a contradiction with 2 5s in one column which cannot be greyed out. So it must be like this instead:

4:

The 6 bottom right means the 5 and 6 on the right must be like so. The three above the greyed out 5 means the 3 lower down must be greyed out.

5:

The 8s next to the 6 and 2 that are greyed out means the other 8s must be greyed out. This leads to a 2 also being greyed out.

6:

An 8 under the greyed out 5 top left means a different 8 gets greyed out. Finally we have to use the 'continuous area' rule to finish this off, so no area is isolated. And voila! 22 greyed out squares and no repeating numbers

Now whats the next step....

Answer 3

Is the answer...

SCOTCH PIE ?

I arrived at this answer as follows:

In the lefthand grid, after the 22 squares are shaded, combine the remaining numbers with the corresponding 'L' or 'R' indicators on the right grid, to get the image below.



Step through each row, summing the total or L's and R's in the row to arrive at a single number.
For example, in the first row, we have 7L 6R 4L 5L 1R 8R. This adds up to 1L.

Doing this for each row, we get 1L 9R 3R 11L 19R 8R 23R 26R 14L. Now apply each of those as a Caesar shift to the corresponding ciphertext letter. For example, the first letter in the ciphertext (which, as we were told, applies to the first row) is D. If enciphering, we shift 1L to C, but if deciphering, we shift 1R to E.

Using this method for each character in DXFDMKEPU, we get EOCSTCHPI as the deciphered text. This anagrams to SCOTCH PIE.

The solution to the lefthand grid is as follows. Note that BeastlyGerbil was the first to complete this grid.

First, note the column with three adjacent 2's. If the middle of these were shaded, the other two could not be, and there would be redundant 2's in the column. So the middle 2 CANNOT be shaded, and other two MUST be shaded, to avoid redundancy. Also, because the middle 2 is not shaded, the other 2 in its row MUST be shaded.

No square adjacent to a shaded square can, itself, be shaded, as that would violate the puzzle rules. So none of the 7s adjacent to the upper shaded 2, the 1 adjacent to the lower shaded 2, or the 4 adjacent to the righthand shaded 2 can themselves be shaded. Therefore, we can shade all of the identical numbers in the same columns and rows as these unshaded numbers.

Using the same reasoning, additional protected (cannot be shaded) squares are: the 5 directly above the rightmost shaded 2 and the 6 directly below the rightmost shaded 1. The other identical numbers in the same columns must be shaded. Once this is done, we can also shade a 4 at the top and 5 on the right, using the same reasoning.

Now we can go through the whole grid, row-by-row and column-by-column, looking for two or more of the same digit. If found, and if one of these digits is immediately adjacent to a shaded square, we know that it cannot be shaded, but the other must be shaded. Doing that, the grid now looks like this:

Two repeated numbers are still in the grid: two 7s in the second row, and two 3s in the 9th column. We can use another rule to determine which to shade. In each case, shading a particular one of the 7s and one of the 3s would result in a single isolated white square, which does not connect with the rest of the grid. This violates the puzzle rules, so the OTHER of these two squares must be shaded. Doing so, we get the final grid: