Gillette Single Ring- No Barrel Serial

Hello, quite a while ago, I acquired a Gillette Single Ring in Box at a Flea Market for 2 dollars. I thought it was a killer deal back when I didn't really know much about old stuff, I mean, it looked cool and it had a really neat box. So I've been holding on to it, and for curiosity's sake I've been reading about how to date them.
I think I have this straight, but you seasoned veterans may know better than I do.
I've been trying to find the serial on the barrel, but there's none to be found anywhere. I did however find a serial stamped into the comb. I'll post a picture.
The serial is N369107. If you look very hard, you can barely see it on the bottom half of the comb.
Anyone know anything about this?
Thanks in advance, I've been really coming up short.
It's really a beautiful razor in very good condition. Back when they made things to last....

1920 old type/single ring razor..The numbers were on the either the barrel or the head area. Here is one from France

Thanks Alex! I really had no idea.

The case that you have is from a much older set, originally -- possibly 1904 or '05. The razor and blade boxes you've got could have come together originally, though, in a case like this one of mine, which is also a 1920:

Single Ring box and razor 1906 on the left and a double ring 1903-04 box and razor on the right.

Congratulations--that's a nice razor.

Hm. I think I'm following you.

So the consensus is that the box and razor are not matched? You guys are blowing my mind!

Thanks so much! I'm fascinated by all of this information!