Six-Letter Connoisseur\u27s Ladders

By the time we reach six-letter words, conditions for superior ladders are much improved: nearly one-half of six-letter words are heterograms (all letters are different), the fraction of isolanos (words which have no neighbours) decreases to less than one-tenth, there is a reasonable number of onalosis (words which have neighbours for each letter change), and each word has on average almost six neighbours (one for each letter). In this article, we therefore only consider ladders in which the terminal words are heterograms, with corresponding letters different, and with letters replaced in order. Even so, there are about fifty thousand of them

Four-Letter Super Connoisseur\u27s Ladders

Four-letter words are famously well connected to each other. Fewer than one per cent of words connect to no other, whereas over 70 per cent in each of the four possible positions-on average, there are 23 neighbours for each word. For our present purpose, note that more than three-quarters are heterograms. This means that Connoisseur\u27s Ladders (those with sequential replacement between heterograms, plus a relationship between the first and last words) become commonplace. On the other hand, the number of such ladders is restricted by the relatively small number (fewer than 20,000) of four-letter words available

How Many Anagrams Are There?

This short article was prompted by the formula for Prob(N) in Michael Keith\u27s What are the odds that X is an anagram of Y? in Word Ways, August 2000. It seemed to me that multiplying the values of that function by the square of the number of words of a given length might be expected to give an estimate of the number of words of a given length that are permutations of another word

Bearing servicing tool

A tool for removing and/or replacing bearings in situ is presented. The tool is comprised of a brace having a first end adapted to engage a first end of the bearing housing, and a second end adapted to engage a second end of the bearing housing. If the two ends of the bearing housing are different in configuration, then the respective ends of the brace are configured accordingly. An elongate guide member integral with the brace has two parts, each projecting endwise from a respective end of the brace. A removable pressure plate can be mounted on either part of the guide member for longitudinal movement therealong and has first and second ends of different configurations adapted to engage the first and second ends of the bearing. A threaded-type drive is cooperative between the guide and the pressure plate to move the pressure plate longitudinally along the guide and apply a force to the bearing, either to remove the bearing from its housing, or to emplace a new bearing in the housing