14
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This crossword doesn't have any regular clues, however, all the words are made with the same 7 letters (each of them got a number). No automatic solvers are allowed.

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CSV version:

        1                   4   3   6   7   5   2                           
        7       1                   7               1   2   4   6   7       
    1   4   5   7       2   4   1   2   7                   1               
    4           4   2   7                   4   2   2   7   1   2           
    5       1   2   3   4   5   6   7       3       7       7               
    6   7   7   1   7           3   4   2   7       4   6   3   7   7       
            5       4   5   6   7   3       4       1       2       6       
        3   4   5   2           4   5   2           7               6       4
    4       2           1       2       7               4                   1
    6   3   7   4   1   7       5   7   4   3   1       3                   1
    7           3       3       7       3       5       3       7           7
    5           2       7       1       1   2   4   3   7       5   7   4   2
1   2   4   3       4   5   6   1   2           3   7   1   7   2       3   
            7           7           7       3   7   1   2       7       3   
    4       1       6       6   7   5   7           2           3       4   
    1   2   7   7   3               2   4   3   2   1                   5   
    2       5       4           7       1               2               6   
2   7   1   2       2   7   5   4   5   2               7   3   4   1   7   
    3               7           6           1           7           2       
        6       2               7       3   7   6   7   5   7   3   4   2   7
        3       3       2   4   3   6   7   2           4           2       
        4   3   7   5   4               4               6   3   7   7   2   
        1       7       6               3               7                   
        1                                               3                   
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11
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The matching

1=S, 2=T, 3=R, 4=A, 5=N, 6=G, 7=E. This is a word, of course, because 1234567 is a word in the criss-cross.

How I came to this conclusion

I first looked at the frequencies of the numbers. We get: 1: 30, 2: 39, 3: 34, 4: 35, 5: 20, 6: 19, 7: 59. 7 appeared the most often, so I assigned it an E. Then I assigned T to the next most common number (2). I noticed that 4334567 was a word, so 3 despite its frequency is unlikely to be A or I. I tried O for a bit, but noticed 376753427 so ending with OE would be a bit awkward. So I decided on R as another fairly common consonant. At this point I could see 243672 looking like it could form TARGET, and after that the puzzle was more or less solved, spotting a few more words that needed easy completions.

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3
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7 appears in most words, including three-letter ones, and can appear doubled. Could be O but I'm going with the most likely candidate which is E.
766 is probably EGG, giving 6=G.
67716 (GEE?E) can only be GEESE, so 1=S.
672 (GE?) must be GET, so 2=T.
Only one option for 63772 (G?EET) now: 3=R.
246 (T?G) is TAG, so 4=A.
45673 (A?GER) gives 5=N.

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