Monday, August 10, 2020

Interesting Puzzle Stats

Plates Across America® puzzle

If you have played Plates Across America™ and understand how the game's word puzzles work, you might have asked yourself questions, like "How many puzzles are there?".  In this post, we try to provide some interesting facts about the underlying puzzle data. In case you have not yet played the game, we'll first briefly go over how the puzzles work, however you could also familiarize yourself with the game by trying the free demo here:


Puzzle Rules

A "puzzle" is three letters, where the order matters. A valid answer to the puzzle is a dictionary word in which those three puzzle letters appear and are in that same order. The letters do not have to be consecutive within the word and can appear anywhere as long as the ordering is not violated. Some examples:

    PuzzleValid Answers
    ABTabout, tabletop, bicarbonate
    IOLidol, airfoil, antisocial

Most important to the game is that (generally) the longer answers are worth more than shorter answers. The longer the answer, the further you travel with each puzzle. The goal is to try to cover the distance in a route with the fewest possible puzzles.

There are a few nuances to the scores assigned to the answers so that it is not always strictly that longer ones score higher. For instance, if you just add an "s" to the end of a word to pluralize it, that would have the same value as the non-pluralized word even though it has one more letter. The full run-down of all the scoring rules will be covered in a future blog post.

The Dictionary

The puzzles are derived from the words in the game's dictionary. We built this dictionary trying to cover the most common word usages. For example, though the dictionary does include a lot of medical terminology, it is not trying to be comprehensive to cover all the more esoteric words. 

Our dictionary is not perfect, which is why we provide an in-game feature to allow players to tell us when they find something we are missing. Here's a picture of the "Report Word" link we show in the game:

Suggest addition to dictionary

So, how big is our dictionary? As of this writing, it has 98,614 words. Every week, we add more as our players report words that should be added to the dictionary.

The Puzzles

All the puzzles we show in the game have at least one valid dictionary word as its answer. In theory, there are 26 * 26 * 26 = 17,576 different 3 letter combinations. However, not all these combinations have a matching word, e.g., "WZX". In the end, there are only a total of 14,863 puzzles in our game. 

Some other facts:
  • For the two example puzzles given above, ABT has 1,045 matching words and and IOL has 2,075.
  • The puzzle with the most matches is IES with 18,080 different matching words.

The Answers

If you add up all the valid answers across all of the 14,863 puzzles, you would get that there are 8,071,767 total answers.  That means that the average puzzle has 543 valid answers.

Other facts:
  • With a dictionary of 96,614 words, this means that the average word matches 82 puzzles.
  • Since a valid answer must contain at least 4 characters, the fewest puzzles a word can match turns out to be 3. e.g., The word "pool" only matches POO, POL, and OOL.

Parting Thoughts

We hope you found this small sample of game statistics interesting.  If you have questions or think of anything related to the game's data that you are interested in, please let us know.

Happy Travels!

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