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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 The Essence - re:official solution | Comment 11 of 13 |



I <o:p></o:p>

<o:p> </o:p>

 The Essence <o:p></o:p>

There are numerous flaws in the presentation,
I will address only four :

The number 864, was neither calculated, (explained, proven) nor  used in deriving the puzzle's answer. It is therefore redundant and should have  been either replaced by a word "numerous" or left to be evaluated 
as part of the solving process.


. You use the word "permuted solutions" wrongly.
There are 2 distinct generic (not 2 permuted) solutions,
each creating 432 permuted variations per each generic sample.

  ".It quickly becomes obvious that X can only be 1 or 2, and so by reflection then Y is whatever X is not."  It is indeed very quickly, - it is explicitly declared in the puzzle.<o:p></o:p>

 The whole presentation is a perfect example of 18 lines of  words and numbers where 3 suffice, - a process that politicians practice (e.g. "at this particular point in time" instead of "now"),-  and mathematicians (especially logicians) avoid.   

Adding just one simple sentence after "(11,11,22)"  could constitute a formal proof : 

Since the nine digits (w,e,b,p,a,n,d,i,t) sum up to 44, while all ten distinct digits add up  to 45, then obviously digit 1 is not used and digit 2 is within the set , QED.<o:p></o:p>

Erasing the rest (brevity is the soul of wit) would definitely improve the "official" solution.<o:p></o:p>

<o:p> </o:p>

  Posted by Ady TZIDON on 2013-11-28 03:36:02
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