# The Unfinished Puzzle Section

Simply complete the sudoku and crossword, happy puzzling.

Across
1. Achieved acclaim by being knowledgable about strange apron (3, 6)

Down
2. Explode asteroid five to refrain from inactivity or evade others (5, 4)
23. Clip, rewire, curtail current, repeat (5)

Unassigned
Abbreviation for value disregarding sign of six pack? (3)
Differentiable group three hundred and seventeen head over heels (3)
Invert stripped hypnotist (3)
Not even unusual? (3)
Sequence of games forming part of match with southern alien (3)
Synthesis of Tritium, tungsten, and oxygen into smallest sized compound (3)
Never say it backwards without right for level ground (4)
Plural singular belonging to yours truly! (4)
Scan again partly increments (4)
Being something? (6)
Measure core income trick (6)
Between the menu and the meal one thing goes before another! (7)
Finitely generated free abelian group spanning real space tart's holey top? (7)
Mistakenly disprove supplies (8)
Take all unordered 2-subsets of a set by transforming a savvier transcendental ratio (8)
Used to smell rotten they say it's certainly unmistakable (8)
Beer of infinite acidity, “infinity plus one” (5, 4)
Create cut corn mess covering street (9)
Ordered classification of Cockney girl in process of losing sense (9)
Map to and fro adds charged particle to information about limitless projector (9)
Pigeon-holed personalities in deluded chart races (10)
Staggering credential was woven (10)
Adulterating awkwardly yielded location from angles (12)
Introductions for diminutive Asian as new leader of nations (12)
Reason following headless fellows litigating against journal of ship 99 (7, 5)
Confused, blind tourist is short by fifty for generalised functions (13)
Study of arrangements of deranged, manic robotics (13)

$\mathcal f = ??\Gamma?????\Delta????\Phi??????????\Gamma???\Gamma????????\Phi???\Delta?$ (8, 7, 10, 9, 9)
$\text{clues} = \mathcal f(\text{clues}, \text{remainder})$
$\alpha = ???\Psi????\Psi?\Omega??\Psi???????\Psi????\Omega?????$ (8, 4, 8, 12)
$h = 15d – d$
$h(α) → ? \space \Box$

Hint 1 (2016-04-23 12:00Z)

Currently the sudoku clues are UNMATCHED, and there are 7 possible "solutions"

Hint 2 (2016-04-24 23:15Z)

I was going to just give the hint "Where do 1 across and 1 down go?", but realised I had made an error - I just edited the numbers of all the clues to be one greater than listed except 1 across (I had edited these on the day I posted due to comments about crossword numbering convention). This hint is therefore even greater (but it's my own fault of course!). Now...
"Where do 1 across and 2 down go?"

Hint 3 (2016-04-25 14:00Z)

What could $\text{clues}$ and $\text{remainder}$ be in the equation $\text{clues} = \mathcal f(\text{clues}, \text{remainder})$?

Hint 4 (2016-04-25 21:05Z)

The partially solved sudoku in the community wiki post at present is:

and is not fully resolved (there are more cells one can logically fill with letters that are not yet present)

• I added the math tag as some knowledge of mathematical objects may be required, but Wikipedia is your friend – Jonathan Allan Apr 22 '16 at 18:46
• Are the Sudoku and crossword related or just two separate puzzles? – Gordon Allocman Apr 22 '16 at 18:48
• @GordonAllocman It is indeed all one puzzle – Jonathan Allan Apr 22 '16 at 18:49
• What's up with the numbering in the crossword? You have a clue for 1 across, but there is no 1 across in the crossword. Also, the downs and across are independent. Eg. 2 across and 2 down are not starting at the same block. – Munir Apr 22 '16 at 19:41
• @humn Yes indeed - but I will say that it is not being used to say "?" is an answer with those number of letters - the answer is one of the sudoku solutions and the crossword solution. – Jonathan Allan May 1 '16 at 14:45

Here's some closure for why that one specific Sudoku board state is the correct one.

First, let's solve those Addendum clues.

$\text{clues} = \mathcal f(\text{clues}, \text{remainder})$

If we take $\text{clues}$ to be $\text{UNMATCHED}$ and $\text{remainder}$ to be $\text{ENSUING LOGIC}$, we can apply $\mathcal f = \text{distinct } \text{ordered } \text{characters } \text{provides } \text{bijection }$ to them.

For each string, remove duplicate letters.
So we have $\text{UNMATCHED}$ and $\text{ENSUIGLOC}$
Next, order them. We get $\text{ACDEHMNTU}$ and $\text{CEGILNOSU}$

From there, we can construct this bijection:
$\text{A} \rightarrow \text{C}$
$\text{C} \rightarrow \text{E}$
$\text{D} \rightarrow \text{G}$
$\text{E} \rightarrow \text{I}$
$\text{H} \rightarrow \text{L}$
$\text{M} \rightarrow \text{N}$
$\text{N} \rightarrow \text{O}$
$\text{T} \rightarrow \text{S}$
$\text{U} \rightarrow \text{U}$

which is equal to $\text{clues}$, and therefore "unmatched". We'll match it soon.

Next up, we have $α = \text{pairwise } \text{read } \text{provides } \text{orientations}$ and $\mathcal h = \text{interlace}$. But what do we interlace?

We take the string $α$ and interpret it literally. Break it up into pairs and we get $\text{PA}$, $\text{IR}$, $\text{WI}$, $\text{SE}$, $\text{RE}$, $\text{AD}$, $\text{PR}$, $\text{OV}$, $\text{ID}$, $\text{ES}$, $\text{OR}$, $\text{IE}$, $\text{NT}$, $\text{AT}$, $\text{IO}$, and $\text{NS}$. We then need to interlace each pair, in other words, cross them. Notice that the first letter in each pair exists in $\text{WONPRAISE}$ and the second letter in each pair exists in $\text{AVOIDREST}$. By placing $\text{WONPRAISE}$ across the top and $\text{AVOIDREST}$ along the bottom of the Sudoku grid, we can use the letters as coordinates. Here's the image with those coordinates circled.

We then get the string:
$\text{T _ M _ H _ A _ M _ _ _ T _ _ M}$
but that just seems like gibberish. We can't really fill that in and make sense out of it.

So let's match the bijection to this! We get:
$\text{S _ N _ L _ C _ N _ _ _ S _ _ N}$

We can then attempt to fill these in if we also apply the bijection to the Sudoku grid and also with how words are constructed in English. Between the $\text{C}$ and $\text{N}$ only has these as possible letters $\text{{E,I,O,U}}$. The only one that fits in the Sudoku is $\text{O}$.

Doing a few more of these, we can end up with:
$\text{S I N G L E C O N C L U S I O N}$

Mapping the letters back to the Sudoku grid, we can solve it and mark the previously posted solution as the "single conclusion".

### Pieces of the puzzle in the order presented, as solved here and in other posts

Across

1. Achieved acclaim by being knowledgable about strange apron (3, 6)
Won praise ("wise" around anagram of "apron")

Down

2. Explode asteroid five to refrain from inactivity or evade others (5, 4)
Avoid rest (anagram of "asteroid V")
23. Clip, rewire, curtail current, repeat (5)
Recur (REwire+CURrent)

Unassigned

Abbreviation for value disregarding sign of six pack? (3)
26 across. Abs (double definition)
Differentiable group three hundred and seventeen head over heels (3)
18 down.     Lie (317 upside down)
Invert stripped hypnotist (3)
16 across. Not (hypNOTist)
Not even unusual? (3)
25 across. Odd (double definition)
Sequence of games forming part of match with southern alien (3)
20 down.     Set (S+ET)
Synthesis of Tritium, tungsten, and oxygen into smallest sized compound (3)
24 down.     Two (T+W+O)
Never say it backwards without right for level ground (4)
5 down.     Even ("never" backwards without R)
Plural singular belonging to yours truly! (4)
28 across. Ones (double definition)
Scan again partly increments (4)
Being something? (6)
21 across. Entity (double definition)
Measure core income trick (6)
12 across. Metric (incoME TRICk)
Between the menu and the meal one thing goes before another! (7)
6 down.     Ordered (double definition)
Finitely generated free abelian group spanning real space tart's holey top? (7)
4 down.     Lattice (double definition)
Mistakenly disprove supplies (8)
14 across. Provides (anagram of "disprove")
Take all unordered 2-subsets of a set by transforming a savvier transcendental ratio (8)
7 down.     Pairwise (anagram of "a wiser pi")
Used to smell rotten they say it's certainly unmistakable (8)
22 across. Distinct (sounds like "This stinked" (sic))
Beer of infinite acidity, “infinity plus one” (5, 4)
3 across. Aleph zero (ale+pH zero)
Create cut corn mess covering street (9)
22 across. Construct (anagram of "cut corn" around "st")
Ordered classification of Cockney girl in process of losing sense (9)
29 across. Numbering ("er" inside "numbing")
Map to and fro adds charged particle to information about limitless projector (9)
17 down.     Bijection ("bit" around proJECtor plus "ion")
Pigeon-holed personalities in deluded chart races (10)
13 down.     Characters (anagram of "chart races")
Staggering credential was woven (10)
15 down.     Interlaced (anagram of "credential")
Adulterating awkwardly yielded location from angles (12)
10 down.     Triangulated (anagram of "adulterating")
Introductions for diminutive Asian as new leader of nations (12)
19 across. Orientations (orient+nATIONS)
Reason following headless fellows litigating against journal of ship 99 (7, 5)
$\unicode{8216}\rm remainder\unicode{8217}$. Ensuing logic (men without M+suing+log+IC)
Confused, blind tourist is short by fifty for generalised functions (13)
11 down.     Distributions (Anagram of "blind tourist is" without L)
Study of arrangements of deranged, manic robotics (13)
8 down.     Combinatorics (anagram of "manic robotics")

$\kern1.2em \mathcal f ~ = ~ ??\Gamma?????\Delta????\Phi??????????\Gamma???\Gamma????????\Phi???\Delta?$ (8, 7, 10, 9, 9)

 f  =  ??Γ?????   Δ????Φ?   ?????????Γ   ???Γ?????   ???Φ???Δ?
S        O    E             S      S           E   O
=  DISTINCT   ORDERED   CHARACTERS   CONSTRUCT   BIJECTION

pairwise   lattice   interlaced   alephZero   alephZero       (false possibilities)
provides                          numbering   numbering
bijection   construct


$\kern1.5em \text{clues} ~~~ = \kern3em \mathcal f \kern4.2em ( \kern3em \text{clues} \kern2.3em , \kern2.7em \text{remainder} \kern3em )$

UNMATCHED =     distinct-
ordered-characters-
construct-bijection ( U N M A T C H E D ,   E N S U I N G   L O G I C )

U  N  M  A  T  C  H  E  D ,   E  N  S  U  I  N  G     L  O  G  I  C
:  :  :  :  :  :  :  :  :     :  :  :  :  :     :     :  :        :
U  N  M  A  T  C  H  E  D     E  N  S  U  I     G     L  O        C  (distinct characters)
:  :  :  :  :  :  :  :  :     :  :  :  :  :     :     :  :        :
:  :  :  A ----:--:--:--:-----:--:--:--:--:-----:-----:--:------> C  (a   o   v
:  :  :     :  C ----:--:---> E  :  :  :  :     :     :  :             l   r   e
:  :  :     :     :  :  D -------:--:-----:---> G     :  :              p   d   r
:  :  :     :     :  E ----------:------> I           :  :               h   e   t
:  :  :     :     H -------------:------------------> L  :                a   r   i
:  :  M ----:------------------> N  :  :                 :                 b   e   c
:  N -------:-----------------------:--:---------------> O                  e   d   a
:           T --------------------> S  :                                     t       l
U -----------------------------------> U                                      i c a l l y)


$\kern1.1em \alpha ~ = ~~ ???\Psi????\Psi?\Omega??\Psi???????\Psi????\Omega?????$ (8, 4, 8, 12)

 α  =   ???Ψ????   Ψ?Ω?   ?Ψ??????   ?Ψ????Ω?????
R       R A     R          R    A

provides   even   distinct   ensuingLogic        (false possibilities)
distinct   ones   pairwise   triangulated


$\kern2.4em h = 15d – d$

$\kern1.8em ~~ = \textsf{15 down} - \textsf{d}$
$\kern1.8em ~~ = \textsf{interlaced} - \textsf{d} = \textsf{interlace}$

$\kern3.4em h ~~ (\alpha) ~ \to ~ ?$

$\textsf{interlace} ~ (\textsf{pairwise read provides orientations}) \to \textsf{single conclusion}$

                        α            Pa ir wi se   Re ad   Pr ov id es   Or ie nt at io ns
WON PRAISE         P  i  w  s    R  a    P  o  i  e    O  i  n  a  i  n
AVOID REST        a  r  i  e    e  d    r  v  d  s    r  e  t  t  o  s
:  :  :  :    :  :    :  :  :  :    :  :  :  :  :  :
( distinct          UNMATCHED         :  :  :  :    :  :    :  :  :  :    :  :  :  :  :  :
ordered       A C D E H M N T U     T  E  M  D    H  C    A  N  M  A    H  U  T  E  N  M
characters    | | | | | | | | |     |  |  |  |   /  /      \  \  \  \   |  |  |  |  |  |
construct     C E G I L N O S U     S  I  N  G  L  E        C  O  N  C  L  U  S  I  O  N
bijection )     ENSUING LOGIC

        W     o      n      P     r     a       i       s      e
-------------------------------------------------------------
A |                   |1 T Pa            |                      |  a
v |      8 N ov       |                  |                      |  :          v
o |                   |                  |15 N io               |  :          :        o
|-------------------|------------------|----------------------|  :          :        :
i |3 M wi             |                  |                      |  : i        :        :
d |                   |            6 C ad| 9 M id               |  : :    d   :d       :
R |     11 H Or       |7 A Pr            | 2 E ir               |  :r:    :  r::   r   :
|-------------------|------------------|----------------------|  :::    :  :::   :   :
e |            16 M ns|      5 H Re      |12 U ie  4 D se       |  :::e  e:  :::   :e  :
s |                   |                  |               10 A es|  ::::  ::  :::s  ::  :s
t |            13 T nt|           14 E at|                      |  ::::  ::  ::::  ::tt::
-------------------------------------------------------------   ::::  ::  ::::  ::::::
P......................................Pa:::  ::  ::::  ::::::
i...................ir::  ::  ::::  ::::::
w............................................................wi:  ::  ::::  ::::::
s.............se  ::  ::::  ::::::
::  ::::  ::::::
R......................................Re:  ::::  ::::::
::::  ::::::
P................................................Pr:::  ::::::
o...............................................................ov::  ::::::
i..............................id:  ::::::
e................es  ::::::
::::::
O....................................................................Or:::::
i...................................ie::::
n...............................................................nt:::
a.............................................at::
i......................................io:
n..................................................................ns


Edit: From my (Jonathan Allan) notes:

• Nicely resolved. And quite a deep overall puzzle, @JonathanAllan, that unfortuately many people stopped working on after the crossword was solved. – Dan Russell May 7 '16 at 1:48

completed crossword:

completed sudoku:

• correct. Can you provide your reasoning for this sudoku solution over any other (the sudoku is not a proper [uniquely solvable] one) – Jonathan Allan Apr 22 '16 at 21:49
• I didn't have any special reasoning for the sudoku, I just solved it in the normal way. If there are other solutions and I happened on the right one, that's luck. I know there's more to this puzzle though, still working on it. – astralfenix Apr 22 '16 at 22:10
• That's interesting, did you use the strategy known as "unique rectangles" at some point? Or "BUG"? These are two strategies I know of which have base assumptions of being proper, and I tried to avoid them in setting up the sudoku. (sudokuwiki.org/Unique_Rectangles, sudokuwiki.org/BUG) – Jonathan Allan Apr 22 '16 at 22:14

Community Wiki answer for crossword clues.

1 Across: Achieved acclaim by being knowledgable about strange apron (3, 6)

Won praise ("wise" around anagram of "apron")

2 Down: Explode asteroid five to refrain from inactivity or evade others (5, 4)

Avoid rest (anagram of "asteroid V")

22 Down: Clip, rewire, curtail current, repeat (5)

Recur (REwire+CURrent)

Abbreviation for value disregarding sign of six pack? (3)

Abs (double definition)

Differentiable group three hundred and seventeen head over heels (3)

Lie (317 upside down)

Invert stripped hypnotist (3)

Not (hypNOTist)

Not even unusual? (3)

Odd (double definition)

Sequence of games forming part of match with southern alien (3)

Set (S+ET)

Synthesis of Tritium, tungsten, and oxygen into smallest sized compound (3)

Two (T+W+O)

Never say it backwards without right for level ground (4)

Even ("never" backwards without R)

Plural singular belonging to yours truly! (4)

Ones (double definition)

Scan again partly increments (4)

Being something? (6)

Entity (double definition)

Measure core income trick (6)

Metric (incoME TRICk)

Between the menu and the meal one thing goes before another! (7)

Ordered (double definition)

Finitely generated free abelian group spanning real space tart's holey top? (7)

Lattice (double definition)

Mistakenly disprove supplies (8)

Provides (anagram of "disprove")

Take all unordered 2-subsets of a set by transforming a savvier transcendental ratio (8)

Pairwise (anagram of "a wiser pi")

Used to smell rotten they say it's certainly unmistakable (8)

Distinct (sounds like "This stinked" (sic))

Beer of infinite acidity, “infinity plus one” (5, 4)

Aleph zero (ale+pH zero)

Create cut corn mess covering street (9)

Construct (anagram of "cut corn" around "st")

Ordered classification of Cockney girl in process of losing sense (9)

Numbering ("er" inside "numbing")

Map to and fro adds charged particle to information about limitless projector (9)

Bijection ("bit" around proJECtor plus "ion")

Pigeon-holed personalities in deluded chart races (10)

Characters (anagram of "chart races")

Staggering credential was woven (10)

Interlaced (anagram of "credential")

Adulterating awkwardly yielded location from angles (12)

Introductions for diminutive Asian as new leader of nations (12)

Orientations (orient+nATIONS)

Reason following headless fellows litigating against journal of ship 99 (7, 5)

Ensuing logic (men without M+suing+log+IC)

Confused, blind tourist is short by fifty for generalised functions (13)

Distributions (Anagram of "blind tourist is" without L)

Study of arrangements of deranged, manic robotics (13)

Combinatorics (anagram of "manic robotics")

Fully filled crossword:

There is no space for the (7,5) clue; 1 Across, and 2 Down have been confirmed as being around the sudoku as per Dan Russell's post.

Partially solved sudoku:

Building on Wesley Situ's good work on the Addendum:

Splitting the first addendum string into the specified number of characters, and taking answers from the crossword of appropriate length as possibilities, we get

??Γ????? (DISTINCT, PAIRWISE, or PROVIDES)
Δ????Φ? (ORDERED or LATTICE)
?????????Γ (CHARACTERS or INTERLACED)
???Γ????? (CONSTRUCT, NUMBERING, or BIJECTION)
???Φ???Δ? (CONSTRUCT, NUMBERING, or BIJECTION)

And then using the greek characters as simple substitutions narrows us down to the correct series of words:

Γ must be S
Φ must be E
Δ must be O

Leaving the clue: DISTINCT ORDERED CHARACTERS CONSTRUCT BIJECTION

Applying the same technique to the second series of Addendum characters yields:

• achieved acclaim by being knowledgable ... won praise. confused, blind tourist ... distributions. – astralfenix Apr 22 '16 at 20:17
• @f'' note that 8D was changed to 22D after I was informed of numbering convention – Jonathan Allan Apr 22 '16 at 22:02
• @f'' amazingly the only one left unsolved is a bit of a cheat TBH. – Jonathan Allan Apr 22 '16 at 22:37
• @Munir I missed your question until now. Distinct is indeed correct (if you did not already know from my update with the complete crossword) - it's actually a bit of a cheat "This stinked" (sic) which some people may actually say. – Jonathan Allan Apr 25 '16 at 15:37
• @JonathanAllan I figure, since it didn't get edited. Thanks. – Munir Apr 25 '16 at 15:39

Perhaps the locations of 1-across and 2-down are

around the Sudoku rather than the crossword.

And given that the letters used in the sudoku can spell (as in hint #1):

UNMATCHED, perhaps the 1-across and 2-down answers were intended to lead us to the correct sudoku answer rather than one of the other 6 possible solutions.

Just putting some more thoughts out there in case they might spur anyone forward:

Based on what I wrote in the community wiki, we have a couple clues from the Addendum. The function called $\mathcal f$ comes out to DISTINCT ORDERED CHARACTERS CONSTRUCT BIJECTION. Since we're told that $\text{clues} = \mathcal f(\text{clues}, \text{remainder})$, and the most obvious choice for "remainder" is the answer that we haven't used yet either in the crossword or wrapping the Sudoku, ENSUING LOGIC, then perhaps we need to apply those instructions to that clue. One attempt:

ENSUING LOGIC (DISTINCT: eliminating the double characters leaves...)
ESULOC (ORDERED: alphabetical leaves...)
CELOSU (CONSTRUCT BIJECTION: mapping could lead to...)
C=E, L=O, S=U or perhaps C=O, E=S, L=U

Not sure where that gets us. The second addendum clue, $\alpha$, works out to PAIRWISE READ PROVIDES ORIENTATIONS. We're told h=15d-d, which could be INTERLACE (15-down INTERLACED - D), and then to apply h to $\alpha$, so perhaps we need to mess with INTERLACE.

At the same time, there's a lot of overlap in the letters of WON PRAISE AVOID REST and PAIRWISE READ PROVIDES. Perhaps comparing these sets will be fruitful?

• You are correct about where 1 across and 2 down go, and that these will help the way to yield the correct sudoku solution). I am not sure what your blue entries are, however (they are all uniquely identifiable cells already). Time to follow hint 3. – Jonathan Allan Apr 25 '16 at 15:15
• The answers to 1-across and 2-down share 6 letters, so the blue cells are just the 6 intersections of those same letters. – Dan Russell Apr 25 '16 at 15:20
• Yeah, I didn't see how they would, just that they were in a sense "matched." I'll leave them there so these comments make sense. – Dan Russell Apr 25 '16 at 15:28
• If you break "pairwise read provides orientations" into pairs of letters, in every pair the first letter is in "won praise" and the second letter is in "avoid rest". Maybe each pair is coordinates to a cell in the sudoku. – f'' May 1 '16 at 4:58
• Interesting that "celosu" has the same characters as "clues", plus an O. – Zandar May 1 '16 at 5:01

No one has posted about the clues in the Addendum, so here's my take on them in hopes that others might find a connection between them and the Sudoku puzzle.

The greek symbols and question marks don't make any sense to me, but following the convention of the crossword puzzle clues, the numbers that follow denote the number and the length of the words.

For the function f, we have (8, 7, 10, 9, 9). Using the solutions to the crossword clues, we can put together something like "provides ordered characters numbering bijection". I'm not exactly sure what the correct combination is between the available words, but I think that would lead us to what we would need to get from clues and remainder

For the function h, I think 15d -d translates to crossword word 15 down, which is interlaced and subtract the d, so the function would be interlace

From α, (8, 4, 8, 12) might translate to something like "distinct even pairwise orientations". Using the function h, interlace them for another clue.

• On the right track – Jonathan Allan Apr 26 '16 at 0:10