"Regardless to the fact" vs "Regardless of the fact"

Solution 1:

"Regardless to" doesn't really work, I think—I understand the meaning, but regardless doesn't normally collocate with to, so it sounds odd. To my ears, there's nothing wrong with the first sentence. If you really want to avoid that doubled of, you could try this phrasing:

Some arrangements work better than others, no matter how many detectors are used.

Note that this is a bit less formal than your original.

Solution 2:

"Regardless to" is the one that sounds awkward because it's utterly ungrammatical.

However, "regardless of", aside from being grammatically correct, sounds quite appropriate to my ear.

Some arrangements work better than others, regardless of the number of detectors used.

Here's an equally formal alternative you might want to consider:

Some arrangements work better than others, whatever the number of detectors used.