More Word Network Spasns in the OSPD

In the February 1989 Word Ways, I examined various word networks based on words from the Official Scrabble Players Dictionary (OSPD). To refresh the reader\u27s memory, a word network consists of a set of words of a given length that can be joined by word ladders (single-letter changes). Each pair of words in a word network can be connected by a minimum-length ladder (one which cannot be reduced by any alternative ladder)

Lewis Carroll\u27s Word Ladders

My knowledge of the history of word ladders comes from two books The Magic of Lewis Carroll by John Fisher (1973), and The Oxford Guide to Word Games by Tony Augarde (1984). It is not necessary to describe word ladders to the readers of Word Ways; in any event the concept should be ovbious from the examples. Carroll started writing about what he called Doublets in 1879; he had originally called them Word Links. The idea, of course, is to find the shortest ladder between a pair of words

Four-Letter Word Network Update

A word network is a set of words of a given length in which any two words differing by only one letter in a single position (such as aunt and runt, or hire and hare) are connected by a line. Using three lines, one can trace out a path leading from any word in a network to any other word in the same network. THe terminal words, together with the intermediate words in the path, form a word ladder, well-known since the days of Lewis Caroll. This article updates a number of recent articles in Word Ways describing the properties of four-letter word networks and ladders

Directed Word Chain Networks (Part 3)

This is the third of a series of articles on directed word chain networks; the first two can be found in the August 1991 Word Ways. Specifically focussing on (8, 4) word chains, it is divided into two sections. THe first introduced a two-dimensional construction called a mesh; the second updates and extends Part 2, using an enlarged word list. All terms are defined in Part 1

Word Network Spans in the OSPD

A word network is a set of words of a given length in which any two words differing by only one letter in a single position (such as aunt and runt, or hire and hare) are connected by a line. Using these lines, one can trace out a path leading from any word in a network to any other word in the same network. The terminal words, together with the intermediate words in the path, form a word ladder, well-known since the days of Lewis Caroll (who invented the concept, calling the terminal words doublets and the intermediate words links). There are, of course, many possible word ladders joining any pair of words in a network, but for each pair a minimum-length ladder can be found. If one now considers all pairs of words in the network, one or more of these considers all pairs of words in the network, one or more of these pairs will have a minimum-length ladder that is exceeded in length by no minimum-length ladder belonging to some other pair; that is, these pairs possess the maximum minimum-length word ladders taken over all word-pairs. The number of lines in this maximum path is called the span of the network

Literary Cryptarithmetic By Computer

In the November 1989 Word Ways, Peter Newby presented a set of literate cryptarithms. This name was coined by Newby, but is is a well-known concept: these are cryptarithms in which the code letters form interrelated words. They are discussed in Mathematics on Vacation (1966) by Joseph Madachy, editor of the Journal of Recreational Mathematics. He calls them alphametics, a word coined by J.A.H. Hunter in 1955

Chinese Stepladders

Word Ways readers are familiar with Lewis Carroll\u27s word ladders. As a variation, Dave Morice suggested in the August 1989 Kicksaws a game which he called Stepladders. Two words join only if the letters which are exchanged are adjacent to each other in the alphabet

More Insertion-Deletion Networks

This is the second of two articles that investigate various properties of the insertion-deletion (ID) networks. The first article appearing in the August 1990 Word Ways, looked at words fully deletable to 2-letter words, as well as words that can be deleted or inserted in every position (charitable and hospitable words). The complexity of the ID network was hinted at with a depiction of the insertion network of CARE

Letter-Shift Words In the OSPD

In the November 1979 Word Ways, the editor explored the subject of letter-shift words (words which can be trasmuted into each other by constant shifts along the alphabet, as CHEER to JOLLY or PECAN to TIGER). Confining himself to the Merriam-Webster Pock Dictionary, he showed that letter-shift words come in 13 varieties, according to the distance shifted along the alphabet. More recently, the topic of letter-shift words was reopened by Dave Morice (who exhibited an analogue device for more quickly finding such pairs) and Anthony Sebastian (who showed how it could be done using a spreadsheet program). About the only thing Sebastian\u27s method for finding letter-shift words can do for a logologist is give him eyestrain. In fact, computer facilities require for the job are less than needed for the spreadsheet. I wrote a program in QUICKBASIC 4.0 which attacked the problem as follows

Word Ladders of Today

In an earlier article, I showed how many of the classic word ladders proposed by Lewis Carroll could be shortened with the aid of the computer. In this article, I use the computer to construct many new word ladders having various characteristics