Equivalent Words from WordWalk Perspective

 It turns out that some WordWalk puzzles have different solutions.  That's because many different can have the same set of unique letters.  E.g., the words 'earth', 'heart', 'rather', 'theater', 'threat' all use the same unique set of letters {e,a,r,t,h}, although some words use multiple instances of the same letter.  'theater', for instance, use e and t twice each.

I call such words equivalent to each other.  Here's another set of equivalent words:{'pressure', 'purse', 'pursue', 'super'}

And yet another:

{'concentration', 'container', 'creation', 'interaction', 'reaction'}

If a WordWalk puzzle is built from any one of a set of equivalent words, it may have the same structure (i.e., be isomorphic) as one built from another from the same set of equivalent words -- but not necessarily!  The nodes will certainly be the same, but the arrows may be different.  

Consider the graph for each of these words below:





Now if you put them all together into a single graph, you get:


See:  https://wordwalk.net for more details.


Comments

Post a Comment

Popular posts from this blog

New WordWalk Format

Image
 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
Read more

Coming Soon: A Change to the WordWalk Points Reward System

Currently, WordWalk starts you off with 0 points and then you get 10 points for each correctly placed subword and an extra 100 for the rootword (which also counts a subword so, in fact, you 110 points for the rootword).  So, for a five-subword puzzle you can get a maximum of 160 points. Moving forward (possibly starting tomorrow) the points system will be different.  You will start out with a certain number of points (say, 100, for discussion purposes).  Then you will get 10 points added to your points stash for each new correctly guessed letter and also 10 points for each new correctly guessed arrow.  These points will not be added, however, until after you've completely and successfully placed the subword in the puzzle graph.  Once that is done you will get some extra points (say, 25) for the subword itself and the new points for new letters and arrows that were obtained while placing the subword. If you fail while trying to place a subword, you won't lose remaining guesses a
Read more

WordWalk Puzzles: 1/26/23

 WordWalk Puzzles for 2023-01-26 at https://wordwalk.net Yesterday's puzzles: English rootword was "CONDITION". German rootword was "ZUCKTET". Spanish rootword was "MORTALES". Kids rootword was "DEPOSIT". #wordwalkpuzzles
Read more