(In reply to

Disappointed! by brianjn)

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 , GIV**EN 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.