Daily Puzzles 2024-05-17

https://www.spaghettispeller.com/todays-puzzles/2024-05-17

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New WordWalk Format

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 Yesterday we implemented a new version of WordWalk , eliminating the drag-and-drop approach in favor of point-and-click.   We have also placed all the candidate letters in a table row above the graph, so now there are no longer any floating letters that have to be dragged and dropped. We have also included the maximum possible score (which varies with each puzzle) so that you can compare your score against the best possible. To help understand how this works, let take a look at the kid's puzzle step by step. Here's the initial set up. Note that there 395 points possible. First we try to spell out "BEER" by selecting the B in the table: Then we select the B in the graph, which gets highlighted in yellow, and the yellow/red coloring for the B in the table reverts to white/black: Since the B is a correct first letter for either of the subwords, it remains yellow/black until the subword is completed.  Since we are trying for "BEER", the next letter is E: Placin...
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A New Feature

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WordWalk puzzles now highlight the letter that starts the hidden rootword by thickening the border of the shape that depicts it. This was due to discovering that it is easy to forget which letter was first after correctly placing the subwords in the graph. E.g.,in today's English puzzle, we have: The first letter of the rootword is H, as indicated by the ovals with the thick borders.  Then, after embedding, e.g., the subword "HALL" into the puzzle, we can still tell which letter is the first letter of the rootword:
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WordWalk Puzzles and Graph Theory

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WordWalk puzzles are word games based on the directed graphs inherent in the spelling of words (in any language that supports alphabetical spelling).  The idea is that the sequence of letters in each word implies a unique directed graph that is unique for the given word.  Letters are assigned unique vertices in the graph and the relation 'is-followed-by' between letters is reflected in a directed graph edge. For example, the word 'jump' would be represented as the graph <V,E> where V={j,u,m,p} and E={(j,u),(u,m),(m,p)}. Pictorially, we might have: (The special diamond shape for the letter 'u' is used in official WordWalk puzzles to indicate that this letter is a vowel.) This directed graph contains only a single path and is perhaps not very interesting because each letter occurs exactly once.  But if a letter occurs more than once, an arrow is drawn from the letter just before the repeat back to the original node for that latter.  E.g.,in the word 'el...
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