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Instructions:

• Four mystery words are replaced with a double question mark and must be deduced by the solver. NOTE: words are not necessarily in alphabetical order after the mystery words are deduced.

• Divide the sixteen words into four groups of four. Each group contains one mystery word.

• Next, fill in the blanks to complete four sentences. Each question mark represents one of the words in the above grid. Words can appear more than once. All four sentences must be sorted in alphabetical order (for instance, if the first sentence starts with GOLF then no other sentence can start with ABSENT)

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    $\begingroup$ Hm. I think I've got good candidates for the mystery words (one group is especially nifty, in my opinion), but I have a hard time to figure out how to complete the sentences. I have a feeling that the sentences describe a well-known paradox that you either know or don't know, like the last stanza here. (On the other hand, I may just be a bit dense, of course.) $\endgroup$
    – M Oehm
    Commented Jul 2 at 6:58
  • $\begingroup$ Time for a small hint maybe? $\endgroup$ Commented Jul 7 at 9:51
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    $\begingroup$ small hint: rot13(rirel zlfgrel jbeq rkprcg bhg vf pbeerpg). $\endgroup$
    – happystar
    Commented Jul 8 at 10:19

1 Answer 1

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[This is a partial answer. I think I have the groups and reasonable candidates for the mystery words, but I'm struggling with filling in the blanks in the sentences.]

Groups and mystery words:

ABSENT, MISSING, REMOVED, OUT mean "not/no longer there".
ACCOMPLISHED, CREEP, CRITICAL, IMPOSSIBLE can follow "mission".
BIND, GOLF, HEMP, JACK use each letter from A to P exactly once.
FOUR, HUNDRED, SIXTEEN, ONE are square numbers.

Of the proposed mystery words, only JACK is certain. The other groups can be completed with various words. I've tried to pick words, that might reasonably fit into the blanks.

"Mission Impossible" is a well-known film franchise and I can imagine that the last sentence reads "... is therefore impossible." I've picked ONE as the square number (which might really be any number), because it looks like the most useful choice.

The one I'm least sure about is the synonym of absent, missing and removed. OUT could fit in one of the double blanks, e.g. "missing out", but LOST, GONE or even NOWHERE could work, too.

The blanks in the sentences:

From the instructions we know that each blank is one of the sixteen words in the connect wall, that words may be used several times and that the sentences are in alphabetical order after the blanks have been filled in correctly.

I think that only the four mystery words are used and that the first word in each sentence is the same. That's a gut feeling and not enforced by the rules of the puzzle. (Most of the given words don't usefully fill the blanks, except the numbers perhaps.)

There's a [mathematics] tag and I guess that the sentences form a well-known logical paradox. (OP has written a similar puzzle that in my opinion relies on knowing the final question, a well-known mathematical problem; that question can't be worked out just from solving the first part of that puzzle.)

For example, the sentences could be: "Jack is correct. Jack is (somthing something). Jack is not (the same two words). (Something) is therefore impossible." The (something something) would have to be before "not" in the alphabet.

If we do have to use some of the given words, the sentences might describe numeric equations. But still, I think the four mystery words should be used at least once, otherwise that part of the puzzle would be pointless. And in that case, I can't fit the only mystery word I'm pretty sure about, JACK, in anywhere.

Oh, another thought: There's a [lateral-thinking] tag and the sentences don't have punctuation. I've assumed that each line is a sentence, but that need not be the case.

So, yeah, a lot of hemming and hawing. I'm probably on the wrong track here. I'm sorry that I can't offer anything better than these ramblings.

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    $\begingroup$ This looks very similar to my own thoughts :) rot13(V unqa'g gjvttrq gur 'bapr sebz N-C' pbaarpgvba; V jnf ybbxvat ng pbafbanag-ibjry-pbafbanag-pbafbanag jbeqf naq cynlvat jvgu ZNGU nf n gbcvpny bcgvba; V yvxr gur arngarff bs WNPX gubhtu... V jnf guvaxvat bs FHOGENPGRQ sbe gur 'zvffvat' pngrtbel ohg gvzr jvyy gryy jung gur orfg guvat vf gurer...) $\endgroup$
    – Stiv
    Commented Jul 2 at 16:48
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    $\begingroup$ Along the lines of what Stiv said, could the replacement for OUT be rot13(ZVAHF) $\endgroup$
    – hexomino
    Commented Jul 2 at 17:59
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    $\begingroup$ Rot13(V jnf guvaxvat gung gur zlfgrel jbeqf unir fbzrguvat gb qb jvgu gur neenatrzrag. Yvxr ebj pbyhza qrqhpgvba fbzrubj (fvapr BC jevgrf "qbhoyr dhrfgvba znexf" (cbffvoyl 11,22,33,44) Nyfb, fvapr gur svefg vafgehpgvba fgnegf ol fnlvat qrqhpr gur zlfgrel jbeqf naq gura vafgehpgf hf gb gb tebhc gurz va 4f. Nf vs gur qrqhpgvbaf bs gur zlfgrel jbeq jnfa'g eryngrq gb gur tebhcvatf bs 4f, V zrna. V pbhyq or jebat bsp ohg whfg fbzrguvat gung V gubhtug bs.) $\endgroup$ Commented Jul 3 at 11:07

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