It was extremely difficult to spot this w1 (=an extinct bird) w2 (=in the middle of, surrounded by) the bushes, but once the notorious gunman from Perfection,Nev. w3 Gummer saw it, the bird's w4 was inevitable.

w1,w2,w3,w4 are four-letter words
w2 and w3 are jointly composed of 8 distinct letters.

If the letters in the words are replaced by nine digits (distinct digits representing distinct letters)- the following equations come true:

w3+w1=w2
w3-w1=w4

q1: What digit in the alphametics is not represented by a letter?
q2: What is the bracketed word in the title ?

Hint (not mandatory):
4 968301 9401 94Y 625301 Y628 3I5

The above senseless, albeit grammatically correct, sentence may be of help.

(In reply to A happy ending (spoiler) by Steve Herman)

Hi, Steve

 in the  "cryptations" .  That would be a D4 puzzle, precluding "software only" solutions and forcing you to browse the web, at least to get the gunman.

In the process of debugging my own puzzle, which I often do by trying to solve it without any "a priori" assumptions I have realized    that if the solver gets just one word wrong , he is off the track and it might be very difficult and discouraging to go on

With this in mind and knowing that the experienced solvers think "out of box" I added few clues:  " Trouble",  the senseless sentence, only 9 digits in use, w2 and w3

using 8 out of nine … 

Just looking on    4 968301 9401 94Y 625301 Y628 3I5 implies 4=A and 94Y=MAY , then  6=O, the most frequent letter to follow Y, --O—L-  becomes TROUBLE(not happy ending) and the rest is history. 

So actually it is a D2 PUZZLE, if you by-pass the sequence implied by the text and 

use your senses ,- how to solve.

I don't know whether your chain of thought is isomorphic with the one I have described (please comment), but anyway you did an
 excellent job.

Edited on December 15, 2013, 2:45 am

Posted by Ady TZIDON on 2013-12-15 02:37:47