There are currently 118 elements in the Periodic Table, each Symbol consisting of one or two letters.
Some words can be constructed from the set of these Symbols and some cannot.
For example "calculus" has two "elemental representations":
C Al C U Lu S
C Al Cu Lu S
Moreover we will add one point to a word's "score" for every letter in the word which can appear as the first letter of a two-letter symbol and also as the second letter of a two-letter symbol in different valid elemental representations of the same word.
The word "calculus" scores zero points because the only difference between its two reprentations is C U vs Cu.
On the other hand, "snow" can be:
S N O W
Sn O W
S No W
Since the letter "n" appears both in Sn and No, "snow" gets one point.
Your challenge: If k is the maximum score of the set of all words in the English language, try to find an example word for each score from 1 to k.
Charlie's solution is outstanding.
Unfortunately, this was not the scoring system I had in mind, but now that I have re-read my description of the scoring system, I didn't explain it very well. Therefore, because of my poor explanation, I consider alternate scoring systems to be equally valid. However a different method of scoring would no doubt lead to a different 'winning' words.
I'll try to further explain the scoring method I had in mind by " ... first letter of a two-letter symbol and also as the second letter of a two-letter symbol in different valid elemental representations of the same word."
Designate the letters of the N-letter word as a(1), a(2), ..., a(N). The i-th letter contributes a 1 only if the 2-letter combo a(i-1)a(i) is an element and also a(i)a(i+1) is an element and also each appears in a different representation of the word. The maximum score for an N-letter word is N-2, since the first and last letters, a(1) and a(N), always contribute 0 to the score. This is because the first letter (a(1)) can never be the second letter of a 2-letter symbol; the last letter (a(N)) can never be the first letter of a 2-letter symbol. Each other letter (except the first and last) can contribute at most 1 point to the total score. Single-letter symbols such as for Hydrogen, Oxygen, Uranium don't count as the first letter of a 2-letter symbol.
Use "presses" as an example:
P Re S S Es
P Re S Se S
Pr Es S Es
Pr Es Se S
P appears as P and Pr 0 points
R appears as Pr and Re 1 point
E appears as Re and Es 1 point
S appears as S and Es 0 points (Ss would have to be a symbol for this to get a point)
S appears as S and Se 0 points
E appears as Es and Se 1 point
S appears as Es and S 0 points
total score: 3 points
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Posted by Larry
on 2022-07-16 09:21:42 |
Not the scoring method I had in mind, but ...
