Can a 75x75 table (consisting of 75x75 identical square grids) be partitioned into dominoes (1x2 rectangles) and crosses (five square figures consisting of a square and its four neighbors.)

Provide adequate reasoning for your answer.

__Source__: St. Petersburg City Mathematical Olympiad (Russia)

This problem is kinda like Kakuro, Sudoku AND Hanji combined!

Rules:

1) No row or column may contain the same digit more than once. Zero is not used.

2)The numbers above and to the left show the totals of each group of adjacent numbers in the relevant column or row.

3) Within a given row or column there must be one or more blank squares separating the groups from each other.

Example: 5 13 12 might lead to

5-4126--93

6 15 2 10 5 11 16
8 30 14 14 19 17 10 27 13
18 9 27 8 6 12 15 20 4 3
+--+--+--+--+--+--+--+--+--+--+
3 10 18 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
12 18 6 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
20 7 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
5 3 6 8 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
25 19 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
13 13 14 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
6 29 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
18 7 19 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
9 23 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+
7 7 14 | | | | | | | | | | |
+--+--+--+--+--+--+--+--+--+--+

*Note: A page listing out sums possibilities is here*