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Authors

Rex Gooch

Abstract

As we move from 9- to 8-letter words, the number of neighbours per word increases by one-third, so the number of ideal ladders (those which change every letter in the minimum number of steps) jumps from about 50 to a few thousand. The percentage of heterograms doubles to a significant 20 per cent, so that the number of ladders between heterograms (with just one unchanged letter in the eight steps) explodes to over six thousand. Combining these facts, for the first time we find ideal ladders between heterograms, thus fulfilling the first three conditions for the elusive Connoisseur's Ladder. The few previously-published 8-letter ladders (see Long Examples in "Snakes and Ladders" in the May 1998 Word Ways) contain a number of ideal examples, but the terminal words are not both heterograms, nor especially related.

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