# How many times can the “X” tile be used in one Scrabble game?

How many times, at most, can the “X” tile be used to form new words in one game of Scrabble? Show the resulting board, and provide a list of each new word formed, in the order played.

For example, in the resulting board below, the “X” can be used three times by adding one or two letters during each play to form these new words: OX, POX, and EPOXy. (The lower case “y” indicates a blank tile was used for “Y”. This is just for illustration, since an actual “Y” tile is still available to be used.)

+---------------+
|               |
|               |
|               |
|               |
|               |
|               |
|               |
|     EPOXy     |
|               |
|               |
|               |
|               |
|               |
|               |
|               |
+---------------+


Rules:

Use an English language 15 x 15 Scrabble board and letter tiles.

Only legal Scrabble words may be formed on each play, and words can be checked at https://scrabble.hasbro.com/en-us/tools. Bluff (phony) words are not permitted.

There is one “X” tile in Scrabble, worth 8 points. The number of times you “use the ‘X’ tile” means you count the number of times the “X” tile contributes 8 (or more) points to the score of any new word you play. Scoring is otherwise irrelevant to this puzzle, and bonus squares do not affect the outcome, so an "X" tile counts at most once per new word played. Blank tiles may be used, but if a blank tile is used as an “X”, then it does not count as using an “X” tile.

You can pick any tiles from the bag (you’re not drawing at random), you should achieve the desired result in the fewest plays possible, and you should stop making plays when you’ve achieved your highest possible “X” word count. This will keep the resulting board reasonably simple.

You must follow all other Scrabble rules, including: The first play of the game must cover the center (star) square. You cannot exceed the standard “Scrabble tile letter distribution” (shown at https://scrabble.hasbro.com/en-us/faq).

I believe there is just one set of “X” words that leads to the highest possible count, and finding that set of “X” words is the main challenge here. If there are multiple ways to form a board with that set of “X” words, then I will accept the first valid solution posted.

• Are point tiles taken into account? For example, if the X falls on a double score tile but is used to make fewer words, is that considered a better option? Jul 27 '20 at 14:11
• @Bewilderer No, bonus squares do not affect the outcome. I'll clarify the wording. Jul 27 '20 at 14:49
• "no-computers" tag might be relevant, Ive already thought through the method for a script that could solve this. Jul 27 '20 at 15:46
• Computers, and/or a word list, are welcome! This could be hard to solve otherwise. Jul 27 '20 at 17:01

I recently downloaded a file starting "Collins Scrabble Words (2019). 279,496 words. Words only." for ... other purposes.

A simple program to scan this showed

4 chains of length 8:

AX => MAX => MAXI => MAXIM => MAXIMA => MAXIMAL => MAXIMALIST => MAXIMALISTS
EX => SEX => SEXT => SEXTO => SEXTON => SEXTONS => SEXTONSHIP => SEXTONSHIPS
EX => LEX => FLEX => FLEXI => FLEXION => FLEXIONS => REFLEXIONS => IRREFLEXIONS
EX => LEX => FLEX => FLEXI => FLEXION => FLEXIONAL => INFLEXIONAL => INFLEXIONALLY

Of these, only

MAXIMALISTS

is acknowledged as an official scrabble word by the specific checker you specified should be used in your question. Thus, unless your scrabble words dictionary has a longer chain not found in mine, my initial guess was that the intended answer must be:

16 for 2 instances of the word "MAXIMALISTS" built up according to the chain shown, and crossing at an X in the middle of the board...

But hang on...

there are only 2 M tiles in the scrabble set - that would need 4.

No problem:

we can use blank tiles for the other 2 Ms.

Lets try fitting that on the board with legal plays as the only chain of plays.

Oh dear... we need to move it to another position. This should work:

... if we can play the first "AX" after a series of other legal plays, without interfering with the ability to make all the other plays. In order to reach the 'A' we must cross from the starting square, which as "MAXIMAL" is built up one letter at a time, means crossing at the first S or the T.

After a little more computer-assisted dictionary searching, I found the following:

This takes a total of

19 plays of which 16 score the X.
1. "BY"
2. "ESPY"
4. "AX" (first play that scores the X)
5-19. Add more letters following the sequence (AX => MAX => MAXI => MAXIM => MAXIMA => MAXIMAL => MAXIMALIST => MAXIMALISTS) to make two instances of MAXIMALISTS.

... which would all be fine until I did a last-minute check and found that:

"DI" isn't in your scrabble words dictionary.

So a last-minute substitution of a different word into the same constructions gives my final answer as:

19 plays of which 16 score the X.
1. "BY"
2. "ESPY"
3. "ATHLETE"
4. "AX" (first play that scores the X)
5-19. Add more letters following the sequence (AX => MAX => MAXI => MAXIM => MAXIMA => MAXIMAL => MAXIMALIST => MAXIMALISTS) to make two instances of MAXIMALISTS. 2-letter words formed from "ATHLETE" above the horizontal instance are all valid.

Post-script: you can find the C# program I used (and dynamically modified as the solution progressed) at https://pastebin.com/nxwVCbC6

• ... and if you care at all about the score, you could replace the second word played with one of 5 letters beginning with the same 2 letters, and the first word played with something that your new word can be played onto, so that both instances of the long word land their final letter on a double word score. There may also be other higher-scoring options for the first 3 words played. Jul 29 '20 at 12:07
• Well done! You found my intended set of "X" words, and you placed them in fewer plays than I expected. Jul 29 '20 at 14:57
• If the Collins list indeed omits DI, that would be a shame, as DI was in the Chambers-based SOWPODS list. Aug 23 '20 at 12:42
• @RosieF Collins list includes 'DI', which is why my program initially found it. The site specified in the question (hasbro) does NOT recognise it, which is why I couldn't use it in a final answer to this question. Aug 23 '20 at 19:26

Here's a first guess after a quick browse of a list of official scrabble words that contain the letter X

14 times

Image source

Each word can be played one at time or together. The verified words to play are:
AX [or XI] > AXIL > AXILLA > AXILLAR > AXILLARY > MAXILLARY > SUBMAXILLARY [or PREMAXILLARY]
There are enough letters for these two words without using blanks

Room for improvement

Finding any x-word which can be broken into at least 8 separate x-containing words will produce a count of 16 (the word can be played twice), assuming it fits on the board and there are enough letters

The minimum length for such a word is 9 letters, assuming one letter is added per turn and the first word is a two-letter x-word

So, carefully perusing the list linked above (by hand or program) starting with 9-letter words may yield an improved result

• I think you meant your diagram to cross at the X - after all, there's only 1!
– Stiv
Jul 28 '20 at 17:12
• @Stiv Thanks! I've updated the image
– user69943
Jul 28 '20 at 17:20