when you say "For 18 words, 1500 years", you mean to just generate ALL possible combinations, right??
if my secret/mnemonic phrase is:
"cat15 cat2 cat3 cat4 cat5 cat6 cat18 cat8 cat9 cat10 cat11 cat12 cat1 cat14 cat7 cat13 cat16 cat17"
and my script generate that exact sequence as the 4th result, is it not the same ??
have i found it in some seconds?
Yes, in theory you could find the right combination with the first attempt as soon as you begin brute forcing the seed phrase. But the chances of you doing that are so small that it's not worth trying. It could also take thousands of years. Knowing all words (but not the order) significantly makes the task easier.
I am not a mathematician, so someone who knows will drop by to mention how much easier. Not knowing any of your words is an impossible brute forcing task though. But if you are only missing the order and have powerful machines, I think it's double within a few years of brute forcing. This is just my amateurish guess.