\$100 Words

My eleven year old daughter came home with a homework problem. The task is to find \$100 words. A \$100 word is a word whose letters, when assigned values, sum to 100. Each one she finds is worth "\$100" in their little game at school. Okay cool! But the values are assigned like this:

• a = 1


• b = 3

...

• m = 25


• n = 26


• o = 24

...

• z = 2

This is not exactly the most intuitive way to number the alphabet, and it certainly makes it hard to evaluate a given word as the typical mapping we're used to (a=1, b=2...) doesn't help. I gave up after a few minutes and told her she should learn to program to solve the problem.

She wasn't too thrilled with that idea, but here's my simple Haskell solution:

import Char (isUpper)

values :: [(Char, Int)]
values = zip (interleave ['a'..'m'] ['z','y'..'n']) [1..26]
    where
      interleave :: [a] -> [a] -> [a]
      interleave (x:xs) (y:ys) = x : y : interleave xs ys
      interleave _ _ = []

charValue :: Char -> Int
charValue c = case lookup c values of
  Nothing -> 0
  Just v  -> v

wordValue :: String -> Int
wordValue = foldl (\s c -> s + charValue c) 0

goodWord :: String -> Bool
goodWord word@(x:_) = (not $ isUpper x) && wordValue word == 100
goodWord [] = False

main :: IO ()
main = interact (unlines . filter goodWord . lines)

Just feed it a list of words, like the handy /etc/dictionaries-common/words and away it goes...

$ ./DollarWords < /etc/dictionaries-common/words 
abductor's
abductors
abidings
...

$ ./DollarWords < /etc/dictionaries-common/words | wc -l
652

So, if I was to unleash this on her poor unsuspecting teachers, her team would rocket ahead with \$652,000! But I guess that wouldn't be fair since she didn't write the program...

I'd love to see other versions of solutions for this problem.