The Rev Dodgson said:

Bubblecar said:

The Rev Dodgson said:

The word must have at least one unique letter and at least one letter that only appears in two words. The possible words are:

BAIT, RIGS, FAKE, SCAM.

If she got a T she would know it was BAIT.
If she got an I Doug would get an A or an S and not know the word.
If she got an A Doug would get an I, T, or S and know the word, so she still wouldn’t.
If she got an S Doug would get an R, I, or A. He wouldn’t know the word if it was A or I, so he must have got an R, so the word must be

RIGS.

If Amy has B, Bob has T, Carol has A and Doug has I, Doug wouldn’t know whether it was BAIT or RIGS.

If Amy has G, Bob has R, Carol has S and Doug has I, Doug wouldn’t know whether it was BAIT or RIGS.

That’s how we know Doug didn’t get I.

So what did Bob get, in your scheme?