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57 58 [ 67] 68 69 76 77 80 81 82 56 [ 59] 66 65 70 75 78 [ 79] 84 [ 83] 55 60 [ 61] 64 [ 71] 74 [...] ... 85 ... 54 [ 53] 62 63 72 [ 73] 30 ... ... ... 51 52 ... ... [...] ... [...] ... ... ... 50 [...] ... 1 [ 2] [...] ... ... ... [...] 49 ... [ 5] 4 [ 3] ... ... ... [...] ... ... [...] ... [...] ... ... ... [...] ... ... [...] ... ... ... [...] ... ... ... ... ... ... ... ... [...] ... [...] ... ... ... 93

    57    58  [ 67]   68    69    76    77    80    81    82
    56  [ 59]   66    65    70    75    78  [ 79]   84  [ 83]
    55    60  [ 61]   64  [ 71]   74  [...]  ...    85   ...
    54  [ 53]   62    63    72  [ 73]   30   ...   ...   ...
    51    52   ...   ...  [...]  ...  [...]  ...   ...   ...
    50  [...]  ...     1  [  2] [...]  ...   ...   ...  [...]
    49   ...  [  5]    4  [  3]  ...   ...   ...  [...]  ...
   ...  [...]  ...  [...]  ...   ...   ...  [...]  ...   ...
  [...]  ...   ...   ...  [...]  ...   ...   ...   ...   ...
   ...   ...   ...  [...]  ...  [...]  ...   ...   ...    93
 

And here is a grid of all numbers that are the same in all solutions.

57 58 [ 67] 68 69 76 77 80 81 82 56 [ 59] 66 65 70 75 78 [ 79] 84 [ 83] 55 60 [ 61] 64 [ 71] 74 [...] ... 85 ... 54 [ 53] 62 63 72 [ 73] 30 ... ... ... 51 52 ... ... [...] ... [...] ... ... ... 50 [...] ... 1 [ 2] [...] ... ... ... [...] 49 ... [ 5] 4 [ 3] ... ... ... [...] ... ... [...] ... [...] ... ... ... [...] ... ... [...] ... ... ... [...] ... ... ... ... ... ... ... ... [...] ... [...] ... ... ... 93

No other solutions were found, so this is the unique solution.

In total 8 solutions were found. The numbers 86-100 can be reversed in all of them reducing the total to 4. Two of these are obtained by reversing 8-16 and 8-22 of the solution above. Here is a fourth type, I do not see how this can be obtained from the first:

    57    58  [ 67]   68    69    76    77    80    81    82
    56  [ 59]   66    65    70    75    78  [ 79]   84  [ 83]
    55    60  [ 61]   64  [ 71]   74  [ 29]   28    85   100
    54  [ 53]   62    63    72  [ 73]   30    27    86    99
    51    52    45    44  [ 43]   42  [ 31]   26    87    98
    50  [ 47]   46     1  [  2] [ 41]   32    25    88  [ 97]
    49    48  [  5]    4  [  3]   40    33    24  [ 89]   96
    12  [ 11]    6  [  7]   38    39    34  [ 23]   90    95
  [ 13]   10     9     8  [ 37]   36    35    22    91    94
    14    15    16  [ 17]   18  [ 19]   20    21    92    93