A Misspelled 10-Square

Here's a 10-square in honor of Rex Gooch. It's what I call a misspelled 10-square. Each row and column is a word, but there may (or may not be) a single transposal of two adjacent letters. Find the misspellings!

aasfetidas
automanula
strulbdrug
fourieirte
emlissaean
tabescnece
indiannses
durreesque
alutaceuos
sagenesess

Boggle and YAWL

I've been using the TWL06 (Scrabble) list. This is fine, but it only includes words up to 15 letters in length. For Boggle this is a minor problem, as it's possible to have 16-, or even 17-letter words if you use the "Qu". So I've switched over to the YAWL word list and started a new billion-board run using the 1992 4x4 Boggle cube set. This is perhaps a bit of second-hard paranoia, as my first billion-board run only found a single board with a 15-letter word - "intergradations".

After 500 million boards, the densest board was:

nslo
eiae
drts
eash

This includes 862 YAWL words.

The board with the highest standard (2311), house (2664) and Fibonacci (3784) scores:

dsti
laee
minr
dest

More on Boggle

As far as I know, there were four different sets of cubes manufactured for Boggle. Two different cube sets for 4x4 Boggle, corresponding to the 1983 and the 1992 versions of Boggle. There were also two different cube sets for 5x5 Boggle, corresponding to Big Boggle and Boggle Master. The more recent Boggle Deluxe has the same cube set as Boggle Master.

Every Kid Loves Boggle

In honor of my friend Rex, I broke out my old Boggle program. After 200 million random boards I've found the following dense board:

dseb
iral
etpm
hsei

Total words = 658

This is also the highest scoring at 2619 points.

This is using TWL06, the acceptable North American Scrabble words, 3 letters or longer, together with the letter cubes from standard (1992) Boggle.

Still runs quite fast, given it was written 10 years ago. I saw some ways to speed it up when I took a quick glance at it, but I can't do anything until after the baseball draft. This was originally meant to be part of an article I was going to write on Boggle, which I will finally sit down and finish in a few weeks.

I love modern computers! Even using a trie compressed into a dawg (directed acyclic word graph) I'm only using 4% of my memory, and I'm only maxing one of my CPU cores.

Remembering Rex Gooch

I found out today that an old friend of mine, Rex Gooch, passed away. I just wanted to say a few words about him to some of my friends who never had the pleasure to know him.

He was from Letchworth, England and a graduate of Cambridge. He eventually developed a passionate fondness for words and word puzzles, something we both shared. My interest eventually led to me becoming a member of the National Puzzlers' League and to the journal Word Ways, which is how I met Rex. At this point in time the Holy Grail of word puzzles was constructing a 10-letter word square, which is a square consisting of 10-letter words reading the same down as across.

Here's an example of an 8-square, found by Richard Sabey:

crabwise
ratlines
atlantes
blastema
winterly
intertie
seemlier
essayers

And a 9-square I found:

karatekas
apocopate
rosecolor
acetoxime
tokokinin
epoxidize
kalinites
atomizers
serenesse

At this point many 9-letter word squares had been found, including Eric Albert's, which had every word in the same dictionary. But no 10-letter word squares.

I, of course, being young and stupid, tried to find one and failed miserably. But this did lead me to propose a probabilistic model of word squares, which fit the available data very well. My conclusion was that you'd need about 90000 different 9-letter words before you should expect to find a 9-letter word square among them, and an astonishing 230000 10-letter words before you'd expect to find a 10-letter word square among them. So it's no wonder that no one had found a 10-letter word square, there weren't that many 10-letter words!

Enter Rex Gooch. He realized that there were, in fact, this many 10-letter words, if you include biological and geographical words. So he meticulously began to gather 10-letter words. He contacted me at this point, and I sent him a copy of a program that I had written that would search every possible combination for 10-squares. I pointed out to him that it'd take approximately a year to run, but always the eccentric Briton, this didn't bother him in the least. He had the desire and the time. The program got modified over that year, in order to handle such things as power outages, and to make it more efficient.

The result?

descendant
echeneidae
shortcoats
cerberulus
enteromere
necrolater
dioumabana
adaletabat
naturename
tesserated

That's 7 dictionary words, 2 geographical words, and one species name. Crazy? Yes. Pointless? Rex didn't think so, and I didn't, either.

He eventually pushed the barrier even further, and by adding the names of people and some foreign words he was able to find an 11-letter word square:

morrismoses
orientirani
rimisurante
reidpainter
inspiradors
stuartmason
miriamgreco
orandarilor
santoseller
enterocoele
siersnorren

He ran his computer for years to find this square.

Rex, thanks for everything. The puzzles you built and the articles you wrote have brought me a great deal of pleasure over the years.