WordWalk Puzzle Solving Strategies (Part 4): Indegree and Outdegree of a Graph

In mathematical graph theory, a directed graph is a structure consisting of two sets, a set of vertices and a set of edges.  (In WordWalk we sometimes call these nodes and arrows.)   For any given vertex, we can ask how many edges lead into the vertex and how many lead away from the vertex.  These two numbers have special names in graph theory:

in-degree of a vertex = number of edges (arrows) pointing toward the vertex

out-degree of a vertex = number of edges pointing away from the the vertex.

 In WordWalk, knowing these two numbers can help you make intelligent guesses regarding the likelihood of a given unknown node being one letter vs another.

For instance, the letter E, is very common, and if you look at all the subwords that contain E followed by another letter that should be approximately one less than the out-degree of that node (one less because it may also happen in the unknown rootword).  Likewise, the number of times E is preceded by some other letter should give you an idea of the in-degree of that node.  This can help you decide where the letter E should go.   

Also, since E occurs quite often in English words, you would expect the total number of arrows (i.e., the sum of in-degree and out-degree) to be higher for the E nodes than, say, for the U node (if there is one).

This is a useful hint for solving WordWalk puzzles.

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