Here are two Crossnumber puzzles.
Across and Down: All numbers must be perfect squares, with 1 down equal to 1 across, 2 down equal to 5 across, etc. Additionally, each of the following two conditions makes the solution unique: (a) the sequence of three shaded squares must spell out a perfect square as well, or (b) no cell should contain the digit 0.
Across and Down: All numbers must be perfect cubes. In the unique solution 1 down turns out to be equal to 4 across, 2 down to 5 across, etc.