# Cipher text on an ancient wall

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).
• When completed, all un-shaded squares create a single continuous area. (Example)

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.

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

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'...

• If this is the correct answer, in my opinion YOU should receive the checkmark. Solving the enigmatic portion of this puzzle, and most others, is much more challenging than solving the preliminary puzzle, which in this case is rather trivial. I don't feel that anyone on this site, myself included, should receive a checkmark simply for posting an incomplete partial answer in which only the easiest part of the puzzle is solved. Apr 24, 2020 at 9:31
• This is the correct answer. @LannyStrack, both you BG got the idea of how the L's and R's are meant to be used. BG mentioned how it should be solved without giving an answer and you were able to get an answer using an idea similar to mine. Stiv was indeed the first to find my final answer. I don't know who deserves the check most, but I think normally, the first to get my answer should get the check (i.e. Stiv). Apr 24, 2020 at 9:38
• @eyl327 - I completely agree. Apr 24, 2020 at 9:40
• @eyl327 Well, it's entirely your shout. I'll edit my answer to include an image of BG's puzzle solve and a reference to his answer. Just didn't want to crash the party... :)
– Stiv
Apr 24, 2020 at 9:54
• Ahhh very nice!!!! @eyl327 I’d say Stiv deserves it or you could create a community wiki so that there’s a correct answer and everyone gets credit. Stiv got the final answer here though, and the grid wasn’t the hard part to solve so I think he should get it! Apr 24, 2020 at 11:27

EXCELLENT

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

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

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....

• I've found what you're missing to get the final answer - feel free to incorporate it into your solution for completeness; this time I didn't get to the initial puzzle in time to solve it myself, so it would be unfair of me to snipe you! :)
– Stiv
Apr 24, 2020 at 9:14
• Okay, I ended up editing my answer to point towards yours for the first part after encouragement from the OP. Hope you don't mind! :)
– Stiv
Apr 24, 2020 at 10:21
• @Stiv not at all!! I was thinking in the complete opposite direction, you deserve the credit! I’ll edit in the answer and link your solution but you still solved half if not more, and the grid wasn’t too difficult so IMO you deserve the tick too :) Apr 24, 2020 at 11:31

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.