Problem 61060. Popular Word Game™ Distance

Professor Ned, who holds the Nedowed Chair of Crackpot Mathematics at the University of Nedsburg, has recently discovered the daily word puzzle Popular Word Game™ published by the Nedsburg Times. He has become so obsessed with it, he is trying to pioneer a whole new field of math based around the idea of a Popular Word Game distance metric: the distance between two points x and y is calculated using the rules of Popular Word Game to score x as a guess for the solution y.
In Popular Word Game, the elements, x(j), of x (which would be letters in the game) are scored using these rules:
  • If x(j) = y(j), then x(j) is shown as green (correct)
  • Otherwise, if x(j) = y(k) for some k ≠ j, then x(j) is shown as yellow (correct value/letter, but wrong location)
  • Elements of y can be used only once as a match
  • Precedence goes first to green matches, then to yellow
  • Evaluation goes in index order (left to right)
  • Otherwise, x(j) is shown as black (incorrect)
In Professor Ned's metric, the elements of x are assigned numeric values according to these same rules, with green = 0, yellow = 1, black = 2. The distance between x and y is then the sum of these individual distance values.
Example
Diagram showing how the distance is calculated for an example with x = [4 3 2 4 2 3 1] and y = [3 1 2 4 1 4 4]. First, the third and fourth elements of x and y are matched and shown as green. Then the first element of x (4) is matched to the sixth element of y. The second element of x is matched to the first element of y. The seventh element of x is matched to the second element of y. These are all shown as yellow. The remaining elements of x are shown unmatched. The two green elements score 0, the three yellow elements score 1 (each), and the two black elements score 2 (each), for a total of 7.
x = [4 3 2 4 2 3 1];
y = [3 1 2 4 1 4 4];
d = PWGdist(x,y)
d =
7
Assumptions
The vectors x and y will be nonempty numeric row vectors of the same length.
Solve

Solution Stats

52.75% Correct | 47.25% Incorrect
Last Solution submitted on Nov 16, 2025

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programming wordle

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