I made three assetions: One thing I suspect however is that both of you (Dudeney and you) can't be right.
The four denominators 257, 809, 562, 795 are mutually prime, i.e., not two of them have common factors, except for 1.
The fractions should add up to 1, right?
You only addressed the last two :) So I am not quite certain whether your solution is right. Is it?
Yes, I missed the last couple of sentences in Dudeney's problem. There were a few left over that were divided equally. So the sum must not be 1.