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First things first, your ever so helpful nonogram. It's got what you need. enter image description here

That should help you sort through this to get your words for the ladder.

4687043851356807498045680642604256148950054205817162311154811546033200909410247081150107615124153210302114565151011511915121049921611212105021541458901239145711501201032145101500106615015471701306380183210654818015011750561105530178981323103228041451215011520011241655001064012501156504526132621017716115151620518408406021680543214581104680585608495158410214415607062151054818766054160051912866052510

So once you have your words, your ladder to solve, easy enough:

enter image description here

Text Version:
_ _ _ _ _ - Your first word
_ _ _ _ _ - Slow down
_ _ _ _ _ - Courage
_ _ _ _ _ - Serious
_ _ _ _ _ - Marks or Incline/Decline
_ _ _ _ _ - Open forest space
_ _ _ _ _ - Pleasure
_ _ _ _ _ - Drive with a stick
_ _ _ _ _ - Positive qualities
_ _ _ _ _ - Forests
_ _ _ _ _ - Communicate
_ _ _ _ _ - Invertebrates
_ _ _ _ _ - Paperwork to fill
_ _ _ _ _ - Unyielding to pressure
_ _ _ _ _ - Project from a gun
_ _ _ _ _ - Loss of job
_ _ _ _ _ - Your last word

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2 Answers 2

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With help from @Meta45, I managed to work out the entire word ladder save for the first and last words:

????? - Your first word
BRAKE - Slow down
BRAVE - Courage
GRAVE - Serious
GRADE - Marks or Incline/Decline
GLADE - Open forest space
GLADS - Pleasure
GOADS - Drive with a stick
GOODS - Positive qualities
WOODS - Forest
WORDS - Communicate
WORMS - Invertebrates
FORMS - Paperwork to fill (found by @Meta45)
FIRMS - Unyielding to pressure (found by @Meta45)
FIRES - Project from a gun
FIRED - Loss of job (found by @Meta45)
????? - Your last word

@Sp3000 then found the first and last words:

BROKE and FIXED

All that remained was to figure out how to obtain those words from the number sequence. Thanks to the hints, and @Beastly Gerbil's existing answer, I realized that

You have to take every fifth number of the sequence. This gives you 01000010011100100110111101101011011001010100011001101001011110000110010101100100, which is clearly binary.

Split into sections of eight (i.e. bytes) and you get 01000010 01110010 01101111 01101011 01100101 01000110 01101001 01111000 01100101 01100100. I can't check yet, but I assume that when converted into a string this spells out "BROKEFIXED".

I need to stop doing puzzles in reverse.

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    $\begingroup$ probably "loss of job" is "fired", "paperwork to fill" is "forms" and "unyielding to pressure" is "firm_". However, I cannot fully get the steps. $\endgroup$
    – Meta45
    Commented Mar 7, 2017 at 10:41
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    $\begingroup$ Based on that ladder I'm going to take a guess that first/last is BROKE / FIXED :P (probably wrong, but I felt like saying it) $\endgroup$
    – Sp3000
    Commented Mar 7, 2017 at 11:52
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    $\begingroup$ @F1Krazy It's okay, I figured it may have happened, but I didn't want to make the hints impossible so it was bound to happen with all you smart people... And my hint for the numbers is -th $\endgroup$
    – n_plum
    Commented Mar 7, 2017 at 13:40
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    $\begingroup$ Yup, every 5th should give you the binary sequence, hence the 8 as a hint, and brokefixed should be what you get. Nice work $\endgroup$
    – n_plum
    Commented Mar 7, 2017 at 14:43
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    $\begingroup$ @n_palum As a bit of puzzling feedback, in general the word ladder clues should match the tense/plurality/word form of the answer. For example, "courage" would ordinarily clue BRAVERY, whereas for BRAVE you'd want to clue with "courageous". $\endgroup$
    – Sp3000
    Commented Mar 8, 2017 at 2:42
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Nonogram solution:

enter image description here

So

5 - and (thanks @Roger) - 8

Step by step (along the same lines as this step by step)

Grey represents an empty square, and black indicates a filled square.

STEP 1: The Defo Nos

The first step is to fill in all the squares grey which definitely aren't filled in (Note I missed one, the first column which is fixed in step 3. This does effect Step 2 but not much):

enter image description here

STEP 2: Mid Grid

Now fill in the squares which are included in all possible solutions for a row/column. There are several in each and the block in the middloe helps a lot in the rows. We can already see the shape:

enter image description here

STEP 3: I Rowed down the Columns

After this there are a lot nearly complete. We can fill in a lot of greys and squares

enter image description here

STEP 4: Number of squares left diminish as we come to a finish

From here it is plain sailing. We get the final answer:

enter image description here

Now I'm not sure, but maybe we need to look through the 5s and 8s?

4687043851356807498045680642604256148950054205817162311154811546033200909410247081150107615124153210302114565151011511915121049921611212105021541458901239145711501201032145101500106615015471701306380183210654818015011750561105530178981323103228041451215011520011241655001064012501156504526132621017716115151620518408406021680543214581104680585608495158410214415607062151054818766054160051912866052510

The rest was solved by F1Krazy:

Taking every fifth number gives binary for BrokeFixed. This gives the completed wordladder:

BROKE - Your first word
BRAKE - Slow down
BRAVE - Courage
GRAVE - Serious
GRADE - Marks or Incline/Decline
GLADE - Open forest space
GLADS - Pleasure
GOADS - Drive with a stick
GOODS - Positive qualities
WOODS - Forest
WORDS - Communicate
WORMS - Invertebrates
FORMS - Paperwork to fill (found by @Meta45)
FIRMS - Unyielding to pressure (found by @Meta45)
FIRES - Project from a gun
FIRED - Loss of job (found by @Meta45)
FIXED - Your last word

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    $\begingroup$ I think the middle symbol is meant to be "and". I've seen people do ampersands that way before. $\endgroup$
    – Roger
    Commented Mar 6, 2017 at 21:50
  • $\begingroup$ Or may be we need to divide those numbers in groups of 8*5/5*8 as the total number of digits are 400 $\endgroup$
    – Techidiot
    Commented Mar 7, 2017 at 9:45
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    $\begingroup$ It's worth noting that there are 85 5s and 8s, which is the same number of letters in the word ladder (5*17 = 85) $\endgroup$
    – Sp3000
    Commented Mar 7, 2017 at 11:52
  • $\begingroup$ @Sp3000 My hint for the numbers is to maybe think less of the literal numbers, maybe more like spacing ;) it was totally a bizarre by chance thing that the numbers added up to the letters $\endgroup$
    – n_plum
    Commented Mar 7, 2017 at 13:27
  • $\begingroup$ @n_palum added step by step. Same as previous one basically :) $\endgroup$
    – Beastly Gerbil
    Commented Mar 7, 2017 at 20:11

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