You can "close" the 2DS using the SLEEP slider.
The puzzles will lose the original meaning nevertheless.

E.g.
Another code's puzzle where you try to stamp something by closing the DS, is logical when the DS is really closed, one screen over the other.
You should be able to do that with the SLEEP slider, but it won't make sense.
Now for the puzzle where you should look at the reflection of the top screen in the lower screen, that one would be really hard to figure out.