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Upon Reflection (Posted on 2013-11-22) Difficulty: 3 of 5
The Alphametics:
WED + TAB + PIN = X j k Y
DEW + BAT + NIP = Y k j X
..... when considered concurrently have 864 solutions.

In the totals X=1 and Y=2 or X=2 and Y=1, and j and k are distinct integers represented in the set of variables.

Why can X and Y never equate to W, T, P, D, B or N? The digits 0-9 are all available but there are no leading zeroes.

See The Solution Submitted by brianjn    
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Some Thoughts re: Disappointed! - I am not | Comment 5 of 13 |
(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 , 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.

  Posted by Ady TZIDON on 2013-11-25 02:45:58
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