A sesquipedalianist Boggle puzzle

During my analysis of the effects of playing Boggle with different letter distributions, I simulated more than 50,000 games of standard 4-by-4 Boggle. One statistic that I was tracking was the longest word found across each of the data sets. Invariably, each data set got stuck at a maximum word length of 11 letters. (In the Big Boggle simulations, the solver found words as long as 13 letters.) I was really hoping for something longer, but rather than keep running simulations until I finally find some 12-letter word and have it turn out to be something disappointing, like BORINGNESSES, I've decided to embed one 16-letter word in a Boggle grid and present it below as a puzzle for your solving pleasure.

Good luck!

The Boggle cube redesign and its effect on the difficulty of Boggle

I wanted to buy a copy of Boggle. This seemingly simple mission was complicated by the facts that a) there are different kinds of Boggle out there and b) I like to make things complicated.

If you exclude variations such as Big Boggle and the recently introduced 6-by-6 Super Big Boggle and just limit yourself to the original 4-by-4 Boggle configuration, there are three principle versions of Boggle:

1) Boggle Reinvention (now sold as just "Boggle") - While the new sealed case design and the integrated timer mean that you don't need to worry about losing any of the pieces, there are reports that it is possible for two dice to become jammed together in such a way that it is essentially impossible to separate them without opening up the case and destroying the game. In my opinion, Boggle should not be a game that can break.

2) Plain old Boggle, made from about 1976 to 1986 (which I will call "classic Boggle").

3) The version of Boggle sold from 1987 to ~2008 - essentially the same as classic Boggle except that the letter distribution on the cubes was completely redesigned. I'll call this "New Boggle".

Below, you can see a side-by-side comparison of the classic and new sets of Boggle dice.

Classic Boggle Dice	New Boggle Dice
AACIOT	AAEEGN
ABILTY	ABBJOO
ABJMOQu	ACHOPS
ACDEMP	AFFKPS
ACELRS	AOOTTW
ADENVZ	CIMOTU
AHMORS	DEILRX
BIFORX	DELRVY
DENOSW	DISTTY
DKNOTU	EEGHNW
EEFHIY	EEINSU
EGKLUY	EHRTVW
EGINTV	EIOSST
EHINPS	ELRTTY
ELPSTU	HIMNUQu
GILRUW	HLNNRZ

To help visualize the differences between these distributions, I sorted the classic letter distribution by number of letters (shown on the left below) and used that order to sort the new letter distribution (shown on the right).

<= Classic New =====>
EEEEEEEEEE EEEEEEEEEEE
  AAAAAAAA AAAAAA
   IIIIIII IIIIII
    OOOOOO OOOOOOO
     LLLLL LLLL
     NNNNN NNNNNN
     SSSSS SSSSSS
     TTTTT TTTTTTTTT
      DDDD DDD
      RRRR RRRRR
      UUUU UUU
       BBB BB
       CCC CC
       GGG GG
       HHH HHHHH
       MMM MM
       PPP PP
       YYY YYY
        FF FF
        KK K
        VV VV
        WW WWW
         J J
         Q Q
         X X
         Z Z

In some ways (such as increasing the number of Ts and Hs), the new distribution is closer to the letter frequency in English words, but that motive alone would not explain why the number of As was decreased and the number of Os was increased. It has been suggested that this change was designed to reduce the frequency of harder letters (like K and G) and make finding words easier.

One other interesting property of the new set of dice is that since it concentrates certain letters all on the same die, it is never possible to make words that combine F and K (like FAKE, FORK, SKIFF,...) or words that combine B and J (JOB, JAB, BANJO,...). It is also not possible to make words with three Ps (like PINEAPPLE) or two Ks (like SKOOKUM, which is a slang term in the Pacific Northwest, derived from the Chinook language, and having multiple meanings: as an adjective it refers to something that is massive or powerful or reliable or simply really cool; as a noun, it can refer to an evil spirit or demon or a monster somewhat like Bigfoot or Sasquatch; it is pronounced /SKOO kum/).

So does this change in letter distribution have an effect on the game? To find out, I ran some simulated Boggle games, generating random boards with each set of dice and using a Boggle solver (written by GitHub user cespare) to determine the number of words in each board, the resulting Boggle score, and the longest word in each grid.

[The default word list used by the Boggle solver only contains words that are 15 letters long or shorter. While it's highly unlikely to find a random 4-by-4 Boggle board containing a 16-letter word, I decided to augment the word list to include 16-letter words, as well as the 17-letter words that could be made with the Qu cube (like QUATTUORDECILLION [which means 10⁴⁵ in the U.S. and 10⁸⁴ in Britain] and SESQUIPEDALIANISM).]

Dice set	Average  # of words	Average  Boggle score	Average length of longest word
New Boggle	~104	~150	6.8
Classic Boggle	~93	~128	6.6

The results show that there are about 12% more words to be found in a New Boggle board. These results are from simulating 10,000 boards for each set of dice, so the numbers in the table may be off by a few percent.

To try to give a little more insight into the difference between these versions of the game, I ran simulations for a New Boggle board in which a randomly chosen cube from a corner of the board was removed. The corresponding results,

Dice set	Average  # of words	Average  Boggle score	Average length of longest word
New Boggle w/o one corner cube	~92	~131	6.6

are really close to the classic Boggle results, suggesting that if you want to make your New Boggle game about as hard as a classic Boggle game, you can just remove a die from the corner of the board before hunkering down to find words.

Out of curiosity, I also ran simulations for 5-by-5 Big Boggle, using the requirement that words be at least four letters long (unlike the three-letter limit in regular Boggle) and using the Big Boggle scoring system, which yielded these results:

Dice set	Average  # of words	Average  Big Boggle score	Average length of longest word
Big Boggle	~190	~395	8.3

(For comparison with 4-by-4 Boggle, if you include the three-letter words that are in Big Boggle boards, the average number of words increases to about 260.)

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Of course, these calculations only confirmed what I already knew: the older version of the game is harder and is the one for me. I bought a copy of classic Boggle from eBay. The dice are made of wood rather than plastic. The timer has sand in it and doesn't make some noise to tell me when time is up. Succinctly, I think it is skookum.

The most difficult Bananagrams challenge I've encountered

Recently, I played a few rounds of Bananagrams. At the beginning of the last game, I flipped over my tiles and only had three vowels. As I continued to peel mostly consonants, I realized that the optimum strategy was probably to dump consonants until I obtained a more reasonable consonant-to-vowel ratio, but I wanted the challenge of trying to finish the game without dumping tiles. But by the end of the game, the situation had not improved: I had 23 consonants and 6 vowels. Furthermore, I also had a Q (with no U), an X, and a Z. I was nowhere close to finishing my grid by the time someone else won.

Here was the set of tiles that I had at the end:

ADEEEGGHKLLMNNNNOQRRRRRSTVXYZ

I decided to save the tiles and try to work out a solution later. I spent some time working on this problem on two consecutive nights. The second night I found a solution that used all the letters but one N, but that seemed to be the best that was possible.

Finally, several days later, I found a true solution. It's possible to vary some of the peripheral words and get alternate solutions, but there is a core structure that I have not been able to alter without rendering the grid uncompletable.

This puzzle can be solved without using any two-letter words or any vowelless words. (I think that violating these constraints would make the puzzle too easy.)

I leave this as a challenge. I will post a solution at some point in the future.

Fun with collective nouns

In England in the Middle Ages, the common practice of hunting led people to coin terms for groups of animals that were specific to each sort of animal (such as a gaggle of geese or a pride of lions). These specialized collective nouns are therefore called "terms of venery" (where "venery" is another word for hunting). In the 14th and 15th centuries, this became a full-fledged fad, with silly terms being coined just for fun and with the process being extended from animals to groups of people.

These terms are still being concocted today. For those of us who like such neologisms, there is now a site dedicated to them: All Sorts (subtitled "a linguistic experiment").

A good place to start is the list of collective nouns sorted by popularity.

Some of my favorites are:

• a seemingly empty room of ninjas
• a brace of orthodontists
• a hush of librarians
• a _____ of mime artists
• a heard of homonyms
• a winter of discount tents
• a clutch of handbags
• a knot of string theorists
• an array of programmers
• a herd of eavesdroppers

The way the site works is that it catalogs whatever suggestions people make on Twitter (when they use the hashtag "#collectivenouns").

Naturally, I couldn't help but suggest a few:

• a closet of skeletons
• a clattering of abacuses
• an epiphany of light bulbs
• an ink cloud of octopuses
• a curiosity of question marks

The All Sorts project is a great concept because it clearly demonstrates the frivolity and playfulness of minting new collective nouns. Try it. It's fun!

A review of the word-tree building game Konexi

I previously posted about how intrigued I was about a new game that involved assembling letters into a precarious tree of words. Now, I have finally played this game (Konexi), and it exceeded my expectations.

The first player places a letter on the table, and then every successive move involves building letters off of that first letter, such that no other letter touches the table. The letters have little notches and also little isolated teeth, like the teeth of a gear, that fit nicely into the notches, while allowing a little bit of movement. By matching up a tooth of one letter with a notch of another letter, you can add the new letter to the tree, subject to the physical stability of the placement.

On your move, you have a choice between two (effectively) randomly chosen letters. You take one and try to add it to the tree in a way that allows you to connect together a set of letters that can be anagrammed to form a word. The letters must be a contiguous set. Your score is the number of letters in the word that you were able to make.

Even once you find a set of letters in the existing tree that you can connect your chosen letter to, to form a new word, it can often be a huge challenge to place that new letter. It must connect one of its notches or teeth to a complementary tooth or notch of one of the letters in your word, and it must result in a balanced structure that continues to stand on its own. Consequently, whenever someone is placing a new letter, there is a tension to the process that is similar to those moments when someone is removing a piece from a Jenga tower (though it is generally not at the Jenga level of pressure). However, Konexi is actually better than Jenga because you have far more options as to where and how you can place letters. It's also a good game for building intuition about concepts like the center of mass of an object.

This game can play out in very different manners, depending upon the structure of the tree that the players form, and the letters that they choose. With enough vowels in your tree, you may find that it is easy to make four- and five-letter words on every turn. If insufficient vowels are available, players may at times struggle to form any words at all.

If someone accidentally knocks down the tree, that player loses three points, and a new tree is started on the next play. Play continues until someone scores 20 points.

This game is basically exactly as cool as it looks, so if you think it might be your kind of game, you will probably enjoy it.

My addiction to, and subsequent recovery from, Drawception

In my last post, I explained the wonderful sentence-illustrating, drawing-captioning game of Picture Telephone. In the wake of the recent brief popularity of a game for mobile devices called "Draw Something", a lone developer created an online version of Picture Telephone called "Drawception". This is not the first such attempt, having been preceded by such implementations as Broken Picture Telephone and Doodle or Die, but it may be the best.

The first night that I played Drawception, drawing anything using a mouse and the simple controls was a struggle. The resulting drawings were crude. My goal that first night was to unlock the ability to start new games (which allows you to write the initial description that seeds the game). In order to unlock this ability, I had to first earn ten points.

While Picture Telephone is a purely cooperative game, Drawception has some competitive aspects, since players earn points when other players vote for their panel. Once the game has reached its pre-designated panel limit (typically 12 or 15 panels at present), the participants, and often other players, read through the game and have the opportunity to click a little upward-pointing thumb symbol on any panel that they want to give points to. Such voting is anonymous and has no direct benefit to the player, except that it lets them express approval and have some influence on what is considered "good" in the Drawception culture.

Many of the drawings from my first night earned zero points, but some earned a few, like my depiction of the description "Rubber ducky, you're the one":

The next morning, enough of the games that I had played in had finished that I had earned the privilege to start my own first game. This is how it turned out:

I was hooked.

This went on to become the top game for the day (where top games are determined by how many people "favorite" it).

As I got better at the game, technical aspects of the game were also being improved. Bugs that slowed down the drawing process and made the results look worse were fixed. Previously you could accidentally paint over minutes of detailed work with one false swing of the cursor; a new Undo button rectified this, expanding the horizon of what could be drawn in ten minutes. Sites of this kind are frequently plagued by trolls who draw offensive panels and try to disrupt games, and one of the biggest successes of the Drawception developer has been implementing a system that mostly negates the effects of such trolling by filtering out or hiding such panels (though there is still enough potentially objectionable material that does not get flagged by the community that children and the easily offended should still not play).

There was a satisfaction that came with contributing panels to ten or twelve games in a night: it felt like an investment because I knew that the next day, I would be getting some funny or entertaining finished games as a result.

One of the highs that I got from playing Drawception was the feeling that, within that small drawing box, I could draw anything. Not just anything that might appear as a Drawception description, but anything that I could conceive of.

The feeling of possibility led me to experiments such as starting games with a particular phrase, just to see what one person's imagination and drawing skill could do with it. If that first drawing then spawned a great game, I viewed it merely as a bonus. When I spotted this kind of description in the pool of possible drawing prompts (and yes, it is possible to develop a sense for which descriptions are the initial descriptions for a game), if I felt that I could do the description justice, I found it satisfying to produce for the game creator a drawing that would make them happy. So, for instance, when I encountered the description "Richard Feynman plays the bongos", I realized that since I knew who Feynman was, I might be the best person playing at that moment to attempt to give it a shot. I found a Google Images result showing Feynman playing bongos to use as a guide and did my best to convey it, but as time was running out, I notice that it was not sufficiently obvious who the bongo player was supposed to be. Then, in a moment of inspiration, I realized that he should be thinking about physics while playing (as this seemed like a very Feynmanesque thing to do), so I drew a thought bubble and put a Feynman diagram inside it.

That my Feynman was subsequently mistaken for Elvis did not bother me. The player who had started the game was pleased and left me a positive comment, which made me smile.

At the peak of my Drawception addiction, I wondered how long it would go on and imagined that it could be part of my daily life indefinitely.

As I become habituated to the initial wonder of Drawception, many of the next hundred games began to seem pedestrian. The games where the same picture and phrase got repeated for most of the 12 or 15 panels, with artwork that was not particularly striking, became old after a while. I yearned for more novelty.

The more common a reference or idea is, the more likely it is for the person writing or drawing the next panel to correctly interpret it. Consequently, it is generally the most widely known references and characters that manage to propagate without distortion across multiple panels. This leads to the majority of games involving pop culture references or Internet "memes" at some point. If you play enough Drawception, you will likely see a lot of whoever the popular characters are at the moment (Batman or Spider-Man or Worf) and you will learn to identify others (such as Trogdor and Nyan Cat and Chthulu and various anime characters).

From this active tide pool of Internet culture emerged a new lifeform: Trouble Muffin. It started out as an in-joke between two friends who played Drawception and created games about someone named "Trouble Muffin". Soon, other players wanted to participate. Trouble Muffin evolved into a muffin with an eye patch and a tough-guy persona. Those who did not recognize him when playing Drawception typically described him as a cupcake or a pirate muffin, but as his fame grew, he became an icon of Drawception. At the peak of his popularity, most of the top games were about Trouble Muffin and his many adventures.

The fun I had watching and participating in the development of Trouble Muffin helped me understand why people can be so enthusiastic about such Internet memes; it's just different when you are on the inside.

Since Drawception is played all around the world, little bits of the language and culture of other countries can manifest during the process of repeated translation between language and pictures. British English has a major presence on Drawception, so if you play long enough you will see police officers described as "bobbies", panties described as "knickers", mathematics called "maths", redheads called "gingers" (though according to this BBC article, the use of the phrase "ginger hair" in American English is growing because "ginger" appeared in Harry Potter books published in the U.S., even though there was an attempt to remove all the British English), and cookies called "biscuits". None of that prepared me for what happened when what appeared to be a speaker of British English encountered a picture of Cookie Monster:

I'm pretty sure that Sesame Street characters are fairly well recognized all over the world, but obviously not quite as well as Robocop is... At least he wasn't referred to as "Biscuit Monster".

As I continued to play, I became more selective in what descriptions I would draw. Only things that I had never drawn before, only descriptions that were inspiring. Sometimes I would skip descriptions for half an hour without finding anything I wanted to draw.

Toward the end, changes to the way the game worked by the developer tended to detract from my enjoyment of the game. Too many games were stuck in the queue, causing games to take days to complete. The blame was placed on descriptions that no one wanted to draw (typically because they were too difficult to draw or to understand). The developer dubbed these "dustcatchers" and decided that whenever a description panel had been skipped by too many players, it would be rejected, and the game would be backed up to the previous panel, which would be reinserted into the pool of available drawings to describe. My first two descriptions after this change were both rejected. I basically stopped playing at that point, feeling that the game was being dumbed down (as recently finished games suggested). The dustcatcher sensitivity was set too high initially, and while this was only a temporary state (I believe the developer must have started silently adjusting it (maybe even the next day)), my addiction to Drawception was finally broken.

It would be easy to say that I am done playing Drawception, that I have lived through a 15-panel pseudo-narrative arc and that my days of playing Drawception are over. But I still check in on the game periodically, and whenever the developer introduces new features, I play with them for a while. Mainly, I prefer to just start games now. It requires very little time and can sometimes yield cool results. And it is ultimately the privilege that motivated me to start playing in the very beginning.

Playing Drawception was a great experience. I got to draw a lot, which is something I enjoy. I honed my ability to paint tiny pictures using a trackpad to levels that didn't initially seem possible. I created popular games and panels. I enjoyed the challenge of trying to read the mind of the player who had drawn a particular panel, to try to come up with the most correct (or most amusing) description of it. And I participated in and enjoyed lots of hilarious and creative games with a good group of players.

The game has now entered a monetization stage, so the nature of the game, and the community around the game, are continuing to change, but there are enough good things about the game that I think I can still recommend Drawception to anyone who wants to try something new.

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• Drawception - the game itself
• The irresistible game of Picture Telephone - My post about the party game that started it all

The irresistible game of Picture Telephone

One of my favorite games is Picture Telephone. Like the children's game of Telephone (in which a message is whispered from one player to the next, becoming garbled in the process, to hilarious effect), Picture Telephone is about transmitting a sentence through a sequence of players. What distinguishes Picture Telephone is that sentences are alternately written and then depicted through drawing. Players are not allowed to write words in their drawings; that would defeat the whole purpose of the game.

For an idea of how it works, consider this mock-up of a typical game:

(This image is from the now defunct site for an online version of Picture Telephone called Broken Picture Telephone. In my experience, actual Picture Telephone games will have complete sentences and will be funnier.)

Inevitably, there will be someone in the group whose drawings of a person talking into a microphone will be mistaken for a person licking an ice cream cone, and someone else in the group will routinely have trouble recognizing what the previous person drew. These players will only make the game more fun.

There are some unwritten rules to this game: Players must legitimately try to communicate the message that they are given. It is very easy to deliberately derail the game and really spoils the fun for everyone. This is fundamentally a cooperative game.

As a corollary, it only makes sense to write as an initial sentence, a sentence that you feel reasonably certain that the next person can draw. Action sentences, like "The picnic was ruined by ants", are good. Don't worry, the sentence will often become more complex and challenging as it makes its way around the circle.

The dynamics of this game are interesting. Occasionally one sentence will make it all the way through the game essentially unchanged. Sentences can even diverge from their original subject and then return to it. Certain concepts seem to have strange attractors in Picture Telephone, such as how many four-legged animals tend to converge to dogs or cats.

The core of the game is the challenge of receiving a written sentence and trying to figure out how you can possibly make a drawing from which the next person can correctly infer the original sentence. I enjoy tremendously this process. The drawing is fun too. Basically, there is nothing about this game that I dislike.

All that you need to play this game is a bunch of 3-by-5 note cards and writing utensils.

As your group becomes more skilled at communicating through drawing, you can use more complex sentences. Consequently, the sophistication of the game scales with the players, like Dixit and chess do.

I have enjoyed this game for years, and I consider it to be one of the most fun games to play whenever a group of seven or nine player is available. It is certainly the game that has made me laugh the most. I have decided to write about it now because I recently spent rather a lot of time playing a new online variation on Picture Telephone called Drawception, about which I will say a lot more in the next post.