Divide the 10x10 square in ten
different,
distinct rectangles so that each one has a dot at a corner.
+---+---+---+---+---+---+---+---+---+---+
| | | | | | | | | | |
+---+---+---+---+---+---+---+---+---+---+
| | O | | | | | O | | | |
+---+---+---+---+---+---+---+---+---+---+
| | | | | | | | | | |
+---+---+---+---+---+---+---+---+---+---+
| | | | | | O | | | | |
+---+---+---+---+---+---+---+---+---+---+
| | | O | | | | | | | |
+---+---+---+---+---+---+---+---+---+---+
| | | | | | | | | | |
+---+---+---+---+---+---+---+---+---+---+
| | | | | | | | | | O |
+---+---+---+---+---+---+---+---+---+---+
| | | | O | | | O | | | |
+---+---+---+---+---+---+---+---+---+---+
| | | | | | | | O | | |
+---+---+---+---+---+---+---+---+---+---+
| | | | | | | O | O | | |
+---+---+---+---+---+---+---+---+---+---+
Label columns from a (left) to j (right) and rows from 1 (bottom) to top (10). Then:
a10 can only be reached from b9: 2x2
a6 can only be reached from c6
if c10 is reached from f9, there's no way to reach b8, so c10 is reached from g9: 2x5
j10 must be reached from j4
j1 must be reached from h1: 1x3
j2 must be reached from h2, so h10 can only be reached from j4: 3x7
At
this point, it's easy to see the rest of the solution: j3 is reached
from h2 (2x3), g8 from g3 (1x6), a8 from f7 (2x6), a1 from c6 (3x6), f6
from d3 (3x4) and d2 from g1 (2x4).
Reasoned solution
