[PW] Word Value Doubling

Sten Thaning sten at thaning.se
Wed Feb 9 14:09:14 PST 2022

I'm not a matematician, but I *think* that any 7 letter word with a word value of 63 will automatically have a reverse-word value of 126.

If we have a seven letter word with the letters (a), (b), (c), (d), (e), (f), (g), and the word value 63 we can give the letters the following values:

First criteria: a+b+c+d+e+f+g=63

Reverse word value = (27-a)+(27-b)+(27-c)+(27-d)+(27-e)+(27-f)+(27-g)
Simplifying: Reverse word value = 189-a-b-c-d-e-f-g = 189-(a+b+c+d+e+f+g)

Since a+b+c+d+e+f+g=63 as per the first criteria, this can be simplified to

189-63 = 126.

Obviously, this only works for 7 letter words.

So the good news is that you only have to look for 7 letter words with word value of 63 and can ignore the reverse value.

 - Sten

> On Feb 9, 2022, at 13:32, Lawrence Currie <currielw at gmail.com> wrote:
> I have a strange question today.
> I'm curious about a phenomenon related to word values.  Normally the word
> value of a word is assigned by giving each letter of the word a value,
> beginning with a =1, b=2, c=3, etc. and adding these numbers for a total.
> I am particularly interested in words that have a word value of 63, and I
> am looking for cases where if you reverse the assignment of values to
> letters (i.e., if now z=1, y=2, x=3, etc.) the word value of the word
> doubles to 126.
> I have been able to find a few examples where this is true:  caspian,
> ireland, siberia, lebanon, senegal, cashier.
> I've noticed that all of these words are 7 letters long, and it would seem
> like the words that meet this criteria would have to be at least 7 letters
> long since otherwise the average value of each letter in the reversal would
> have to be 21 or higher and this would restrict the letters in the word to
> the first 6 letters of the alphabet.  Similarly, once you extend the limit
> on the number of letters in the original word beyond 7, the one with a word
> value of 63,  the number of possible words with this word value begins to
> decrease, and their reverse word value then usually well exceeds 126.
> I am wondering whether anyone has researched this or can come up with a
> means of identifying real words that meet this criteria.  In particular, I
> would like to find a list of words where at least one of the letters is "s".
> Larry Currie
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