What type of puzzle is...

[RossE]

...it when there is more than one word that can solve the same clue? That is, the correct answers are spelled slightly differently, but still fit.

For instance:

Clue: Not very smart

Two possible answers: dummy and dunce

Both answers have five letters and start with du.

I hope that's not confusing.

Thanks in advance.

[Doorbell]

But only one of these possible answers will fit into the rest of the puzzle. You need to get one of the crossing words to figure out which one it is.  This is not an unusual circumstance, so I doubt if anyone has named it.

Lyell

[RossE]

No, Lyell, you don't understand me correctly.

Each of those words can fit the puzzle because they both start with du, and that may be all that's needed for them to fit. That is, the last three letters do not intersect with anything else.

I ask this question because there are specific puzzles that reply on this multiple, similarly spelled answer scenario as the basis of their appeal. There is one in a local paper every week. People pay to make entries and the trick is to come closest to solving the puzzle with the most correct answers.

This type of puzzle must have a name.

If I have a name then I can find some software to help me generate them.

Thanks.

[Doorbell]

Ah, I do remember those from my youth.  I've always considered them scams; I think the "correct" answer depends on the number of entries submitted.  I don't know what they're called -- sorry.