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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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Hints/Tips re: Is this it? ....not quite | Comment 2 of 13 |
(In reply to Is this it? by Charlie)

My solution of the modified post.


The puzzle,  the way it is written, has exactly 0 (zero) solutions .

If none of the consonants in the alphametic is precluded of

representing any digit less than 3 , there is no solution.

I was aware that coping with this restriction is not

possible and therefore  I've tried to word the problem differently to concur with the number of possible solutions, given as 864.

If any solution is found then for the WEB PANDIT (using zero and 8 other digits ) and the said solution fits both alphametics-  then there are 6 permutations due to the order of sumands,  6 due to  the order within the units, 2 for the tens zero staying in the middle- and the last 2  for switching between the results 1**2 and 2**1.  So 6*6*6*2*2=216*4=864.

I understand that you were trying to solve a modified interpretation looking for a generic solution and checking the number of variation it generates. Then you have stopped, printed your result and noted what interpretation of the distorted text it satisfies.

You never tried to find other solution satisfying the same interpretation.

You titled your endeavor "Is it this?", and rightly so  because it is not.

Your generic solution is based on vowels 7,0,4 , consonants(all the remaining digits s except the digit 1),and the 1st line sum of 1232.  while the  additional generic , yielding the same result  is based on vowels 8,0,3, and the same set of consonants (all except 1),

For those not understanding the lingo I enclose both generic samples, yielding 1232 and 2321 for the 1st and 2nd alphametic equations, using the same assumptions Ch.  did.

Ch: VOWELS AIO {0,4,7} CONSONANTS WTP {2,3,6} & DBN {5,8,9}   digit 1 not used

Sample 609 + 378 + 245=1232  
 and      906+873+542=2321


Ady: VOWELS AIO {0,3,8} CONSONANTS WTP {2,4,5} & DBN {6,7,9}   digit 1 not used

Sample 539 + 487+ 206=1232
    and   935+784+602=2321

I also verified absence of other solutions so basically there are only 2 different generic  solutions, bringing the total of solutions  (2 generic sol)*(864 variations / generic sol)= 1728 different sets of solutions.


Here I am going to interrupt my writing ,will revise my text to minimize typos and after short coffee break will present my train of thought for solving manually (p&p, hand calculator and brain).

Rem: to get few samples sets try:   




i=0;  a+e=11

Will continue later.

rem: Edited: CH s.b. Ady and vice versa in the sample solutions.

Edited on November 25, 2013, 3:38 am
  Posted by Ady TZIDON on 2013-11-23 13:48:40

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