The Stew Boy wrote:
Rabscuttle wrote:
bloated - 3
doubles - 3
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×This means that as one of l,t,e,d is in it and f,o,a are in it then b,u,s are not in it.
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×That can't possibly be correct; by that logic, doubles should have scored 1 or 2. (1 for o, 0 for u,b,s, and d,l,e scores 1 or 0, depending on which of l,t,e,d is present.)
Here's the method I use: Given two words, look at what letters they have in common and which differ. This can be a little bit easier if you sort the letters alphabetically, but that's not really necessary.
bloat
ed: b,l,o,e,d a,t
dou
bles: b,l,o,e,d u,s
Score each section:
x1 = score(b,l,o,e,d) y1 = score(a,t) x1+y1 = 3
x2 = score(b,l,o,e,d) y2 = score(u,s) x2+y2 = 3
Now, since x1 = x2, we can use the rules of algebra, ultimately resulting in the equation y1=y2. Going back to our definitions, this means that score(a,t) = score (u,s).
While this doesn't seem terribly helpful on its own, the key here is to realize that the score for a single letter can only be 1 (if the letter is present in the word) or 0 (if it is not). For example, if doubles had scored 5 instead of 3, then we would have ended up with y1+2 = y2 as our equation. This would mean that score(a,t) + 2 = score(u,s) - which would have told us that u,s were present in the word while a,t were not.
This is another way of saying that since doubles scored two more points, and only two letters were different, they have to be responsible for any change in the score.
[Last edited by acrobat at 06-29-2005 12:15 AM]