A blog for fans of Bananagrams, word games, puzzles, and amazing things

Friday, July 24, 2009

Pangrams and what to do when you have too many consonants

Pangrams are sentences that use every letter in the alphabet at least once. Just a few examples:
  • Nth quark biz gyps cwm fjeld vox. (which sounds like the shortest science fiction story ever)
  • Vext cwm fly zing jabs Kurd qoph.
    which I like for the description:
    "An annoyed fly in a valley, humming shrilly, pokes at the nineteenth letter of the Hebrew alphabet that was drawn by a Kurd." (though I prefer the variation: Zing! Vext cwm fly jabs Kurd qoph.)
  • Squdgy fez, blank jimp crwth vox! (Translation: An imperative sentence, commanding one's squashed-down brimless hat to mute the skimpy voice of a Celtic violin. I like this one particularly, as it was made by my current hero, Claude Shannon, whom I will write about eventually, elsewhere.)
There are many more 26-letter pangrams. By adding two letters, one can make parsable pangrammatic sentences like:
  • Waltz, bad nymph, for quick jigs vex!
As pointed out by Robert Munafo: "The fact that so many optimal pangrams exist in English results mainly from its highly complex and flexible grammar, and the borrowing of so many words from other languages."

In particular, all of the 26-letter pangrams above use Welsh words (which have made their way into the English language), since in Welsh, the letter W is a semivowel. These words are a great way of dealing with a consonant-heavy round of Bananagrams. Check them out:
  • cwm (pronounced /koom/) - a Welsh word meaning circular or bowl-like valley, often formed by a glacier.
  • crwth (/krooth/) - an archaic Welsh stringed instrument - like a boxy violin (Parenthetically, writing this definition has inspired me to make up my own (suboptimal) pangram: The King of Quips seized the crwth (like a boxy violin) to jam.)
Another one is bwlch which means mountain-pass, and is kind of fun to say. "I pity the /boolch/!".

Some other good words for getting rid of consonants:
  • hymns
  • fjords
  • rhythms
  • strengths (the longest dictionary word with only one vowel)
The other option when you have too many consonants is, of course, to dump one of them, in hopes of getting some vowels. There are 63 vowels in a Bananagrams set (counting Y as a vowel), so if you pick 3 tiles from a random pool (starting with all 144 tiles), the probability of getting all consonants would be 81/144*80/143*79/142 which is about 18%. (The probability of getting all vowels is 8%.) [The odds could be computed more efficiently if you took into account all the tiles already turned over. This could be useful near the end of the game, but would seem to require superhuman ability to catalog all the displayed tiles. It seems more plausible in the final move of a Scrabble game.]

So, about 80% of the time you'd probably come out ahead (with one or more extra vowels) though possibly with much rearranging to do to use your new tiles. The other 20% of the time you'd just have more consonants and be even more stuck! This is one reason that I generally only dump at the beginning of a game or else when absolutely necessary.