In my last post I discussed the game of hangman, aided by an algorithmic analysis of the winningest words. A few months ago I did something similar with the peg game they have on the tables at Cracker Barrel.  The one where you have a triangle with 15 pegs, with one missing. You remove a peg by jumping over it. The goal is to leave only one peg remaining. I think I won the game the very first time I ever played it, and I don’t think I’ve won since then.

It occurred to me that the game would be easily solved with brute force, and after an hour or two of coding I had done so. However, I never went much farther than that. I had hoped to look for patterns or simple rules that lead to a victory, but never really got very far. But I decided to post what I have here just for the sake of doing so.

         0
       1   2
     3   4   5
   6   7   8   9
10  11  12  13  14

Given the above peg positions, there are four unique starting configurations: you can start with peg 0, 1, 3, or 4 removed. Any other position is a mirror and/or rotation of those four. So I looked at which starting positions were the most likely to win.

Peg 0: 29,760 ways to win of   568,630 games (5.23%)
Peg 1: 14,880 ways to win of   294,543 games (5.05%)
Peg 3: 85,258 ways to win of 1,149,568 games (7.42%)
Peg 4:  1,550 ways to win of   137,846 games (1.12%)

So the moral of the story is: start with a middle edge peg removed, not the traditional configuration of top peg removed. Beyond that, I got nuthin.

Last week Stephanie and I were discussing the game of hangman. I commented that “rhythm” and “myth” are good words because the only vowel is y, and most people try to find the vowel first. I wondered what might be the best possible words.  When I remembered that I’m a programmer, I said “hey, I can write a program to figure this out!” And since I haven’t posted on this blog in quite a while, I thought I’d share.

I found a list of 58,112 words and got to work. I decided to first count the frequency of each letter in the word list.1 I figured that the probability that a letter would be guessed is approximately equal to the frequency of that letter in the language. This could be a bad assumption, but it’s all I had to work with. Then I computed a score for each word by averaging the frequency of each letter in the word. I don’t know that this is the best way of measuring the difficulty of the word, but it’s the best one I could come up with.

Here are the words with the lowest scores (and therefore the most difficult hangman words, according to my algorithm):

fuzz     1.28%
fuzzy    1.37%
buzz     1.39%
why      1.57%
by       1.79%
jazzy    1.95%
jazz     2.01%
huffy    2.02%
buff     2.03%
huff     2.10%
jug      2.17%
jumpy    2.18%
puffy    2.18%
my       2.20%
hubby    2.20%
muff     2.23%
jump     2.29%
puff     2.29%
buy      2.33%
foxy     2.36%

And here are the easiest:

see     10.55%
eerie   10.15%
ere     10.13%
nee     10.08%
sees    10.05%
tee     10.04%
ease     9.81%
eire     9.79%
seer     9.73%
seen     9.69%
eerier   9.67%
tees     9.67%
serene   9.60%
eases    9.56%
settee   9.54%
lessee   9.54%
eel      9.52%
seine    9.52%
seers    9.50%
eeriest  9.47%

While I was at it, I did some other searches on the word list.  Here are the 49 words that have no vowels besides Y:

by
cry
crypt
crypts
cyst
cysts
dry
dryly
fly
fry
glyph
glyphs
gym
gyms
gypsy
hymn
hymns
lymph
lynch
lynx
my
myrrh
myth
myths
nymph
nymphs
ply
pry
pygmy
rhythm
rhythms
shy
shyly
sky
sly
slyly
spry
spy
sty
styx
sylph
sylphs
sync
thy
try
why
whys
wry
wryly

Seventeen words contain all the vowels, including Y:

consequentially
counterrevolutionary
disadvantageously
facetiously
gregariously
heterosexuality
homosexuality
neurologically
neurotically
pertinaciously
precariously
precautionary
questionably
revolutionary
simultaneously
supersonically
tenaciously

And only two words contain all the vowels, including Y, in order:

abstemiously
facetiously

I’ve never thought deeply about this topic before I had a child in the process of acquiring this mangled mess of words we call The English Language... but pronouns are hard you guys!

We sometimes ask Emma who different people in pictures are, so that she can remember the names of those family members she doesn’t see every day. When we get to a picture of Emma, we’ll say “Emma, who’s that?”

“Baby,” she’ll reply.

Then we will say “Emma, that’s you!”

At least, that’s what used to happen. After doing that for some time, if we ask Emma who is in a picture of Emma, she’ll now respond “you!!” And really, that’s our own fault. We told her that it was a picture of You, and so she learned who You was. Apparently You is a baby who looks suspiciously like Emma.

We could try to correct her by telling her it’s “me,” but won’t that get confusing when she actually does learn pronouns? She’ll wonder, “Why did mommy and daddy say that picture of me was a picture of them?” So I guess for now we’ll have to teach her “that’s Emma.” We’re also working on the whole you/me thing with finger pointing, but I’m not sure if it’s too advanced for a twenty-two month old.

Or maybe I could just try explaining that my “you” is your “me” and your “you” is my “me.” There’s nothing confusing about that, right?

Lately we have been getting Emma into a bedtime routine.  Ostensibly, this is to teach (condition?) her into going to sleep easily at night, provided the routine is observed.  In actuality, she doesn’t go to sleep much more consistently than before the routine.  But that’s not really what I came here to write about.  Part of Emma’s bedtime routine is for daddy to read her a story.  (Literacy for the win!)  Tonight I tackled Horton Hears A Who, one of her two Dr. Seuss books (which are by far her longest bedtime stories).  I noticed while reading the book that Dr. Seuss must have pronounced “mayor” as a one-syllable word, a homophone to “mare,” whereas I pronounce it as two syllables, rhyming with “conveyor.”  I’m not sure if I pronounce it differently because I live in a different region, or because the pronunciation has shifted since the book was written in 1954, or both.  (Contrary to what your grade school teachers probably tried to burn into your head, English is a constantly evolving language, and the accepted pronunciation and even meaning of words varies by region and changes over time.)

Here is an example of what I’m talking about from Horton Hears A Who:

There aren’t any Whos!  And they don’t have a Mayor!
And we’re going to stop all this nonsense!  So there!

And here is one more example, which is even odder to my ear:

“So, Horton, please!” pleaded that voice of the Mayor’s
“Will you stick by us Whos while we’re making repairs?”

It is weird to read because “mayor” is used for a rhyme several times in the book, and if I read it so that it doesn’t rhyme it sounds really weird.  In fact, I tend to pronounce the word that is rhymed with mayor (i.e. “there”) as two syllables.

I guess I’m not really going anywhere with this, it was just something I noticed and thought I’d point out.  Other than mayor/mare thing, I didn’t notice any other rhyming problems.  In one place, I think “grocery” must be pronounced as a three-syllable word in order to have the intended rhythm, although I (and most people I know) typically pronounce “grocery” as something like “groshry.”  Oh well, people still consider Shakespeare great poetry, even though many of his rhymes no longer rhyme, so I guess it doesn’t necessarily spell doom.

Over the weekend—while I was back home for my brother’s wedding (some pictures will likely come soon)—I noticed that the organic milk my mom has started buying has a really long shelf life.  The carton I was pouring milk from, for example, didn’t expire for well over a month.  I was curious why this was the case so I did a little research and it seems that this milk has been treated with ultra-high-temperature (UHT) processing, rather than regular pasteurization.  From what I’ve read on Wikipedia, it seems that UHT milk could actually sit at room temperature for months without going bad, and in Europe it’s actually sold unrefrigerated.  Apparently they sell it refrigerated here because Americans wouldn’t buy unrefrigerated milk in test markets.

I couldn’t find a consensus as to why organic milk is UHT processed, though.  Some people said it was because “organic cows” aren’t given antibiotics, so UHT must be used to be sure all bacteria are killed.  Another said organic milk is typically shipped from further away, so they have to use UHT or it would be about to expire by the time it got to the store.  I’m not sure which is the real reason and I don’t feel like doing any more research.

Anyway, I thought that was an interesting fact I’d share with the class.

Some astute individual has probably told you at some point that Eskimos have dozens of words for “snow,” whereas English-speaking individuals only have one.

They lie! (Warning: link goes to a PDF file.)

Also on Wikipedia.

I found this today and thought it was kind of neat.  Many northeastern Indian tribes had names for each of the full moons every year.  Here is a list of the named moons for 2008.  First up is the Full Wolf Moon, next Tuesday.

Maybe everyone else has heard about this, but I never had so I thought I’d share.  It also seems like a great idea for an elementary school teacher to have a little party for the class for each of the moons, while teaching the kids about Indian culture.

I started a list last week of completely random facts that I have learned in the last few months, for the express purpose of sharing them with you, my faithful blog readers.  Without further ado...

When a pilot lands a jet on an aircraft carrier, he does not put on the brakes.  In fact, he throttles his engines to full power.  The is because he might not catch one of the four wires which stop the jet, in which case he must be going fast enough to immediately take off again (otherwise he’d roll off the deck into the ocean).  When such an emergency take-off is required, the pilots call it “bolting.”  In the briefing room, the last pilot who bolted has a mark of shame on his seat (I believe this was a red towel or red jacket or something like that).  I saw this on some Discovery Channel program; I think it was an episode of “Really Big Things” about the USS George H. W. Bush.

When a woman goes to a doctor, no matter what the reason, they ask when her last period was.  I learned this when I went with Stephanie to the emergency room after she fell down the stairs and nearly broke her foot.  I believe she was asked the question at three different times (at check in, by a nurse, and by a doctor).  I failed to see what that had to do with her foot.  It was later explained that they need to know if there is any possibility that you are pregnant before they administer any drugs or take an X-ray or basically do anything.

Squirrels make noise.  That’s something I found out after Punky nearly caught one.  She chased it up a tree, where it turned around about ten feet from the ground and started making a noise that’s kind of hard to explain, somewhere between a high-pitched grunt and a low-pitched chirp.  I’m not sure what natural predator of the squirrel might be deterred by this noise.  Maybe some kind of bird?  Or bats maybe?

When a flag is raised to half-mast, according to US Flag Code, it should be raised all the way to the top, and then lowered to half mast.  When it is taken down, it should be raised to the top before lowering it again.  I had always assumed you just raised it halfway and stopped.  Also, probably the least-observed article in the flag code: “The flag should never be used for advertising purposes in any manner whatsoever.”

Now you can all feel more knowledgeable.

<—- THIS IS NOT LONDON BRIDGE!

Today while making my lunch I had Fuse on in the background, and I saw a video by the girl from Black Eyed Peas called “London Bridge.”  Only, in the video she is not in front of London Bridge.  She is in front of Tower Bridge.  There have been three London Bridges in London.  The first one was the famous one and no longer exists.  The second one is currently located in Arizona.  The third one still stands, but there’s nothing special about it.  You’d think someone involved in the photo shoot would have said “You do realize that’s not London Bridge you’re posing in front of, right?”