The white, black and striped problem

Hello BIOL334 students!

Some of you were very eager to know the answer to the craziest pedigree/gene interaction question that you'll ever see...but I don't want to spoil the fun for everybody else. So, here are a few hints towards the explanation that I find the simplest (but is in no way the only one). PLEASE REALIZE that it's about 5 times harder than a 334-level question, and you did an absolutely fantastic job trying to work it out. You shouldn't fear integrated gene interaction questions anymore!!

HINTS
I'll use symbols B and D for the 2 genes that we all agreed upon, and will define the phenotypes in the following way:

B-D- is black, bbD- is striped and B-dd is white (I hope I remember our pedigree explanation correctly).
The cross B-D- X bbDD gives us:
50% white
10% striped
40% black

We said that it won't (easily) work with 2 genes involved, so we'll have to invoke a 3rd gene... and the 'restrictions' are:
- we need to form a 'new' phenotype in the progeny (that was not seen in the parents)
- we need to make 50% of the progeny of that new phenotype

Remember that, in the world, genes can have more than 2 alleles!
Remember that the pure line needs to be a pure line!
Remember that it IS possible to create novel allelic combinations in the progeny, even with respect to only one gene (remember black X cream gave us some sepia? All with ONE gene!)
Remember that one allelic combination (relative to one gene) can be epistatic to 'everything' else!
Also, notice that all the offspring will be D-, so the white individuals won't be white because of 'dd'. We have to have an alternative way to produce white, and at this point we can disregard D(d) in the analysis, because in this scenario it is now irrelevant.

Have fun and all the best on your final!

Pam