A crossword with a single clue

Question

Each number corresponds to a distinct letter. There are some non-words, such as names of things: people, gods, places, etc. Can you reconstruct the crossword?

In green (1 to 5): Amusing key glues crazy. (5)

Here is a text version of the table, if anyone needs it:

9	10	3	11	12	9	13	14	11	13	■	15
13	9	■	16	11	11	■	11	13	9	6	7
6	2	13	20	3	10	■	16	■	17	9	18
■	6	■	■	12	20	■	16	16	9	17	9
19	20	18	4	11	3	12	■	9	■	■	16
■	11	16	■	■	9	11	■	1	16	20	21
10	13	20	11	1	■	7	6	7	■	3	7
7	■	1	20	13	9	■	13	2	17	■	21
22	11	1	1	11	13	12	7	3	■	6	■
20	19	■	1	2	3	4	5	6	7	8	3
■	■	17	11	19	20	9	■	9	13	9	11
14	9	11	16	■	18	■	10	20	3	20	13
9	10	9	6	23	9	■	■	3	9	3	7
14	■	19	7	11	■	12	6	11	17	■	■
14	13	7	8	3	■	9	13	■	11	15	11
■	7	8	11	3	■	17	9	3	3	11	13
11	3	■	13	5	11	■	21	9	6	11	13

Answer 1

First of all, I see the word "16 16 9 17 9" near the top right. Words starting with double letters are rare, and the only English word which fits this is LLAMA. That gives us:

• 9 = A
• 16 = L
• 17 = M

Then in the upper middle we have a 3-letter word "16 11 11", which must be either LEE or LOO. There are no 6-letter words beginning with AO and ending with A, so it must be LEE, giving:

• 11 = E

Now we have "13 9 7 9" near the top right and "9 13 9 11" on the right-hand side, leading me to the conclusion that these are RAMA and ARAE. So:

• 13 = R

The word "A R 6" in the top left must be ART or ARC or ARK (since E and M are taken). The relative frequency of 6, as well as the words "12 6 E M" and "6 R A 21" in the lower right and "E R A 6 7" in the upper right, suggests that:

• 6 = T

Then "E R A 6 7" must be ERATO (and "7 6 7" in the middle is OTO), giving:

• 7 = O

And "12 T E M" in the lower right must be STEM, giving:

• 12 = S

The combination of "S E 3 S E" at the top and "M A 3 3 E R" at the bottom right makes me quite sure that:

• 3 = N

Now the combination of "23 E N N 5" at the bottom and "T R O 5" in the middle makes me quite sure that:

• 5 = Y

The words "R 2 M" in the middle and "10 20 N 20 R "on the right tell me that 2 and 20 are both vowels, so they must be I and U in some order. The word "T 8 A 20 N" on the right, as well as the relative frequencies of 2 and 20, gives:

• 2 = U
• 20 = I

At this stage I finally solved the cryptic clue:

Amusing key glues crazy = FUNKY (FUN+KY ~ crazy), so

• 1 = F
• 4 = K

Mopping up several in quick succession: "22 E F F E R S O N" is obviously JEFFERSON, "F R E U 19" is obviously FREUD, "E I F F E L T O 8 E R" is obviously EIFFEL TOWER; "10 R I E F" could be either BRIEF or GRIEF, but "T U R I N 10" makes clear which one. So:

• 8 = W
• 10 = G
• 19 = D
• 22 = J

Now "A G N E S A R 14 E R" must be AGNES ARBER and "D I 18 K E N S" must be DICKENS and "F L I 21" must be FLIP and "A G A T 23 A" must be AGATHA, so:

• 14 = B
• 18 = C
• 21 = P
• 23 = H

Finally, "15 O C A L P O P" must be VOCAL POP, so:

• 15 = V

And the final solution is:

A	G	N	E	S	A	R	B	E	R	■	V
R	A	■	L	E	E	■	E	R	A	T	O
T	U	R	I	N	G	■	L	■	M	A	C
■	T	■	■	S	I	■	L	L	A	M	A
D	I	C	K	E	N	S	■	A	■	■	L
■	E	L	■	■	A	E	■	F	L	I	P
G	R	I	E	F	■	O	T	O	■	N	O
O	■	F	I	R	A	■	R	U	M	■	P
J	E	F	F	E	R	S	O	N	■	T	■
I	D	■	F	U	N	K	Y	T	O	W	N
■	■	M	E	D	I	A	■	A	R	A	E
B	A	E	L	■	C	■	G	I	N	I	R
A	G	A	T	H	A	■	■	N	A	N	O
B	■	D	O	E	■	S	T	E	M	■	■
B	R	O	W	N	■	A	R	■	E	V	E
■	O	W	E	N	■	M	A	N	N	E	R
E	N	■	R	Y	E	■	P	A	T	E	R

with the letters appearing in the following numerical order:

F U N K Y T O W A G E S R B V L M C D I P J H (with Q, X, Z not present).

Answer 2

Complete crossword:

 A   G   N   E   S   A   R   B   E   R       V
 R   A       L   E   E       E   R   A   T   O
 T   U   R   I   N   G       L       M   A   C
     T           S   I       L   L   A   M   A
 D   I   C   K   E   N   S       A           L 
     E   L           A   E       F   L   I   P
 G   R   I   E   F       O   T   O       N   O
 O       F   I   R   A       R   U   M       P
 J   E   F   F   E   R   S   O   N       T

 I   D       F   U   N   K   Y   T   O   W   N
         M   E   D   I   A       A   R   A   E 
 B   A   E   L       C       G   I   N   I   R 
 A   G   A   T   H   A           N   A   N   O
 B       D   O   E       S   T   E   M

 B   R   O   W   N       A   R       E   V   E 
     O   W   E   N       M   A   N   N   E   R 
 E   N       R   Y   E       P   A   T   E   R 

In the following, all ? have to be the same letter. Starting with the beginning of Rand's answer:

First of all, I see the word 16 16 9 17 9 near the top right. Words starting with double letters are rare, and the only English word which fits this is LLAMA. That gives us:

• 9 = A
• 16 = L
• 17 = M

Then in the upper middle we have a 3-letter word 16 11 11, which must be either LEE or LOO. There are no 6-letter words beginning with AO and ending with A, so it must be LEE, giving:

• 11 = E

Now we have 13 9 7 9 near the top right and 9 13 9 11 on the right-hand side, leading me to the conclusion that these are RAMA and ARAE. So:

• 13 = R

The word A R 6 in the top left must be ART or ARC or ARK (since E and M are taken). The relative frequency of 6, as well as the words 12 6 E M and 6 R A 21 in the lower right and E R A 6 7 in the upper right, suggests that:

• 6 = T

Then E R A 6 7 must be ERATO (and 7 6 7 in the middle is OTO), giving:

• 7 = O

And 12 T E M in the lower right must be STEM, giving:

• 12 = S

The combination of S E 3 S E at the top and M A 3 3 E R at the bottom right makes me quite sure that:

• 3 = N

Now the combination of 23 E N N 5 at the bottom and T R O 5 in the middle makes me quite sure that:

• 5 = Y

Continuing from there:

MEA?O? looks like MEADOW, so 19=D and 8=W

From there,

MED?A then has to be MEDIA, from where 20=I

This leaves an easy clue in the form of:

This forms EI??ELTOWER, so 1=F to form EIFFELTOWER

Also:

LAFO?NTAINE looks like a misspelling of La Fontaine as La Fountaine, so 2=U (this also fits with the crossing R?M, which makes RUM).

Then:

ARNI?A is easy to fill as ARNICA, so 18=C

From there:

?ROWN crosses ?A??, the most likely letter for 14 is then B (BABB is a surname, and no other letter would fit both).

Continuing:

A?NESARBER can only be Agnes Arber, so 10=G. This also forms TURING and GAUTIER.

Another word:

From DIC?ENS, we have 4=K. This forms FUNK?TOWN in the middle, so 5=Y. This solves the cryptic clue:

Amusing key glues crazy = FUNKY (FUN+KY ~ crazy)

Filling in the last letters:

AGAT?A crosses ?ENNY, so 23=H and we get AGATHA and HENNY.
?EFFERSON looks like it could be nothing but a J, so 22=J.

Delivering the final blow, in the top-right corner we have a word with two different unused letters:

15 OCAL 21 O 21. By elimination of the already used letters, I concluded that this should be VOCALPOP (also forming EVE, TRAP and PATER in the bottom-right corner).