Enigmatics |
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Posted on: Sunday 12/2, 2007; 11:55 AM Create a list of the words, and split the words into their individual characters. Convert the individual characters into Mathematica symbols for use in algebraic computations. Define a patten that matches the vowels. Construct the inequality expression that the word totals of the symbols satisfy. Construct a list of all the symbols other than vowels. Construct the inequality expression that the lower bounds of the (non-vowel) symbols satisfy. Construct all of the alternative inequality expressions that the upper bounds of the (non-vowel) symbols satisfy. There is one (unknown) symbol that is the odd one out, so there are as many alternative inequality expressions as there are (non-vowel) symbols. Compute the solutions allowed by all of the above constraints. The last argument of FindInstance is the number of distinct solutions that are sought, so the actual number of distinct solutions can be found by gradually incrementing this until there is no further change in the output. In this case there are 3 distinct solutions. Compute the word totals of the symbols for each of these 3 potential solutions. Only one of these solutions has a word that has a symbol total of 20, which is thus the solution. |
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