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Numbered Letters (Posted on 2003-07-17) Difficulty: 3 of 5
If each letter has a value (a=1, b=2, c=3 etc.) what words have a total letter value of exactly 100 when you add up all of the letters?

Are there any words that equal 100 if the letter values are swapped (z=1, y=2.....a=26)?

See The Solution Submitted by Lewis    
Rating: 3.2857 (7 votes)

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Some Thoughts mathematical note | Comment 5 of 28 |
No word will be found on both lists, that is the list of words equalling 100 with the initial value assignments and those equalling 100 with the reversed value assignments. That's because in the reversed value, each letter is worth 27 minus what it was worth in the first set. So a word of length n and value v in the original valuation of the letters will have value 27n-v in the reversed valuation. If we want both the old and the new value to be 100 that would be 27n - 100 = 100, or 27n = 200, which is impossible as 27 doesn't go into 200 evenly.
  Posted by Charlie on 2003-07-17 11:50:20
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