(In reply to Disappointed!
The problem as posed is N O T correct! IMHO
The category stated was "Logic". - AND RIGHTLY SO
Charlie was not incorrect to suggest "both" when referencing "Why can X and Y never" THAT WOULD BE ACCEPTABLE ,IF ONE CHANGES THE NUMBER OF SOLUTIONS , GIVEN AS
864 INTO 1728 , the later number provides the true quantity of solutions and fits the requirements with Charlie's interpretation-
another set W, T, P, D, B or N has only digit 2 , not 1&2 and the same result 1232.
I'd be less than professional to berate further!
I BEG TO DIFFER. It would be very professional to either accept my remark or to point out where I err, which is always a possibility.
I suggest a 3rd party resolves the issue.
Perhaps one finds that there are two possible sets of digits for (W, T, P, D, B or N )- one 245679 and the second 235689 , providing 432 solutions for each set and Ady Tzidon erred in counting the permutations for two different generic solutions. -Charlie showed only one sample and did not address the question "Why..etc.
I've solved the puzzle quickly , proving within 2 minutes that
W+ T+ P+D+B +N=33 , A*E*I=0 ,and A+E+I=11 forcing 2 to be included and 1 excluded.- Your basic question was answered.
I am open minded and do not claim to be professional in the science of recreational mathematics.
Still, if I err, - one should convince me by factual arguments,
not by authority.
I would be more than happy to get the issue resolved, -to
find the truth and not to degrade the erring party.