Same Square, One Pixel Over

A $10 \times 10$ grayscale image is black ($0$) everywhere except a solid $4 \times 4$ square of brightness $200$ covering rows 3 to 6 and columns 3 to 6. Rows and columns are counted from $0$. Call it the original.

Two more images are made from it:

• Nudged: the same square moved one pixel right and one pixel down, so it now covers rows 4 to 7 and columns 4 to 7. To a person it is plainly the same picture.
• Ring: the square stays where it was, but its four middle pixels (rows 4 to 5, columns 4 to 5) are switched off to $0$, leaving a hollow frame. That is a different shape.

In the sketch, # is $200$ and . is $0$:

1 original     nudged       ring
2..........   ..........   ..........
3..........   ..........   ..........
4..........   ..........   ..........
5...####...   ..........   ...####...
6...####...   ....####..   ...#..#...
7...####...   ....####..   ...#..#...
8...####...   ....####..   ...####...
9..........   ....####..   ..........
10..........   ..........   ..........
11..........   ..........   ..........

All three images are unrolled row by row into flat lists of $100$ numbers, exactly as a flat layer would receive them. Measure how different two images are, as that layer sees them, by the straight-line distance between their flat lists: take the difference at each of the $100$ positions, square it, add up all $100$ squares, and take the square root.

How many times farther from the original is Nudged than Ring?

Give your answer to 2 decimal places.