The original puzzle contained a mistake, this has now been fixed. I'm really sorry about that!

Last Density™ puzzle is here: Density™ 3 - The Game!, will there be more Density™ puzzles in future? This one may hold the clue to finding out!

If you'd like to create your own Density™ puzzle, the rules are as follows:

1. The resolution of the grid is 72x72 squares
2. No words, text, numbers or symbols can be used
3. The tags should indicate what types of solving strategies are required
4. You must specify the number of words + letters in the final answer

Density Puzzle #4

Oops, something broke!

enter image description here

Final answer: (6, 3)

Hint 1

The word-search is 8x8

Hint 2

The number of words to find in the word-search is clued in the puzzle (the number of words is also, in itself, a hint)

Hint 3

The symbol which clues the missing four-letter word, also clues the direction that the letters should be added to the word-search

Hint 4

The rightmost two 'missing' letters form the middle of the tenth word

Hint 5

How many pieces is the word-search composed of?

Hint 6

The list of words in the word-search is exhaustive at the time of writing, but it's more than likely that at some point in the future, it will no longer be

  • $\begingroup$ Just to check - rot13(gur prageny 4 ner qryvorengryl zvffvat, evtug? Be qb V arrq gb hfr n cebtenz gb svaq gur ynfg barf (qbar ol rlr fb sne)...) $\endgroup$
    – Stiv
    Dec 20, 2020 at 23:11
  • $\begingroup$ @Stiv rot13(gur prageny sbhe ner pyhrq fyvtugyl qvssreragyl...) $\endgroup$
    – Dmihawk
    Dec 20, 2020 at 23:38
  • $\begingroup$ hm, I haven't figured out how Stiv's concern works either. I've also found 8 words, but don't see any connections between them. $\endgroup$
    – Deusovi
    Dec 21, 2020 at 1:10
  • $\begingroup$ if Stiv rot13(unf sbhaq gung gurer n 4 zvffvat yrggref, gura gur svefg ynlre vf cerggl pybfr gb orvat penpxrq, creuncf n cnegvny nafjre pbhyq or funerq?) $\endgroup$
    – Dmihawk
    Dec 21, 2020 at 1:46
  • 1
    $\begingroup$ Ah, I think I have it at last! Will try to match the words up to 'the right ones' as best I can, but I probably won't be 100% spot on! :) $\endgroup$
    – Stiv
    Dec 30, 2020 at 20:31

1 Answer 1


Solved! Note first that this puzzle is tagged as . This means that somehow or other we need to extract a grid of letters from this image. How? Well notice that if you look closely:

There are lines of small shapes hidden in faint colours throughout the image:
Original image with symbol runs circled in different colours

It is likely that these symbols might each decode to a letter that helps to form our wordsearch grid. Furthermore, since these symbols appear in neatly organised lines it is a further possibility that we might be able to assemble together in some way (like a jigsaw) to form that grid.

First, let's try to assemble them into a grid structure...

Noting that the longest symbol-line (circled in purple in the image) comprises 8 images, let's take that one and let it be a whole side of the wordsearch. (Since Hint 1 reveals that the wordsearch is indeed 8x8, this confirms this as a useful strategy.)

We can then squish together the remaining symbol strings, keeping them roughly in their relative positions in the diagram, to produce an 8x8 grid (with a central 2x2 hole) which looks like this:

Symbol runs assembled into an 8x8 grid

How can we read these as letters?

Well, these symbols bear a strong resemblance to the dots and dashes of Morse code, with single-pixel 'dots' and double-pixel 'dashes'. In order to extract valid letters out of them we need to read the horizontal strings from left to right, and the vertical strings from top to bottom (e.g. top left symbol is .-.. while the one immediately below it is -.-.).

Doing this for each symbol produces the following letter grid:

Possible wordsearch letters

With no other segments to fill the central 2x2 gap, we need to add other letters in here - but what letters exactly?! Hint 3 suggests it is related to a symbol in the image. Well, seeing as the clockwise arrow is central to the image, it would probably make the most sense if that were the symbol of interest. The word which would lend itself best to making other words in the grid and also define the symbol itself is (to my mind) TURN, so let's add that to the grid too, starting in the tail of arrow and proceeding clockwise towards its head (as per Hint 3):

The complete wordsearch grid

Treating this letter grid as a wordsearch, there are several words that are immediately obvious (helpfully confirming our choice of cipher), although not all of them are necessarily relevant. However, a bit of thought suggests what we should probably be looking for here...

- Hints 2 and 5 suggest there should be 13 words to find, since the wordsearch comprises 13 pieces...

- Hint 4 suggests specifically that the tenth word should be RENTER, a synonym of tenant...

- Hint 6 suggests the wordsearch theme is potentially something from popular culture - some kind of list that may continue to grow with future instalments...

Combine all of this information with the knowledge that we are looking for a final answer of the form (6,3) and I believe the wordsearch theme must be:

DOCTOR WHO, the British science fiction TV show! To date, thirteen actors have played The Doctor (in the official canon), the tenth of whom was David Tennant, and it is very probable that once the current Doctor (Jodie Whittaker) calls time on playing the role it will be given to another actor so the series can continue.

Knowing this, then, we now need to find:

13 words which relate to each of the names of the 13 actors to have played The Doctor. And here they are:

The completely solved wordsearch...

1. William Hartnell = HEART
2. Patrick Troughton = FEEDER
3. Jon Pertwee = CHEEKY
4. Tom Baker = BREAD
5. Peter Davison = HARLEY (like Harley-Davidson)
6. Colin Baker = CAKE
7. Sylvester McCoy = REAL
8. Paul McGann = FILM (since McGann appeared only in a one-off film version, not the TV series)
9. Christopher Eccleston = BERNIE (like Bernie Ecclestone of Formula 1 fame)
10. David Tennant = RENTER (synonym of 'tenant')
11. Matt Smith = COMMON (as 'Smith' is a very common surname)
12. Peter Capaldi = HAT
13. Jodie Whittaker = CHOC (Whittaker's is a chocolatier and confectioner)

Finally, to remark on the title question:

In all likelihood, there will indeed be more actors who take on the role of Doctor Who - thanks to The Doctor's ability to regenerate their body when it gets worn out, the role is able to be passed from one actor to the next and the change in physical appearance explained away as a plot point. All of this explains why the show has been on our screens since 1963 (with some breaks) and holds the Guinness World Record for being the longest-running sci-fi TV show in the world!

  • $\begingroup$ @user39583 Ah I did list that first one, just missed it on the diagram. Will fix that up. I left out the third one you mention deliberately as it doesn't fit my pattern and I was hoping someone might be able to find a way that the bottom-right missing letter is an H... $\endgroup$
    – Stiv
    Dec 21, 2020 at 13:09
  • 1
    $\begingroup$ Wow! Awesome progress @Stiv :) I can confirm that rot13(lbhe zbefr pbqr vagrecergngvba vf pbeerpg), I will add a hint to the puzzle to hopefully make the next step more clear $\endgroup$
    – Dmihawk
    Dec 21, 2020 at 22:01
  • 1
    $\begingroup$ @Stiv the puzzle has been corrected, as I spotted a mistake. I'm really sorry about that and hopefully it hadn't led you astray! :'( $\endgroup$
    – Dmihawk
    Dec 21, 2020 at 22:51
  • 1
    $\begingroup$ @Dmihawk Okay, I'll fix up my answer to match the new image when I can, and see if anything strikes me about the corrected grid... $\endgroup$
    – Stiv
    Dec 21, 2020 at 22:52
  • 1
    $\begingroup$ @Dmihawk Gah, of course - got too focused on 'trout'! $\endgroup$
    – Stiv
    Dec 30, 2020 at 23:49

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