Constrained Pyramids

By Thorpe, Susan | Word Ways, February 2005 | Go to article overview

Constrained Pyramids


Thorpe, Susan, Word Ways


Word pyramids, in which a letter is added at each step and the letters rearranged, will be familiar to the readers of Word Ways. The aim has been to construct a pyramid with as long a base word as possible, ideally with all words from a single dictionary. Ross Eckler constructed an excellent pyramid, without any plurals, with the 17-letter base word ANTICEREMONIALIST (Word Ways 79146), only slightly marred by the inclusion of the non-dictionary RECLAMATION1ST which seems a perfectly good inferred word. Two pyramids of Kyle Corbin's appeared in WW88075, both with a 17-letter base word, one pyramid with three plurals and the other with five plurals. In WW2003021, Darryl Francis offered the first pyramid with an 18-letter base word PRESENTATIONALISMS. This pyramid included five plurals, two of which were straight pluralisations of the adjacent word.

The pyramids offered here are not aimed at having the longest base word. They are special, however, in that each of them abides by one or more of a range of constraints. Most of the words used below are taken from the Oxford English Dictionary, Second Edition. The sources of non-OED words are given at the end.

Let us begin with a pyramid which describes itself.

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In these pyramids, each word starts with the same letter, and each word ends with the same letter.

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In the first of these two pyramids, each word both starts and finishes with the same letter, E. In the second pyramid, the second and penultimate letters are all Es. The letter E does not appear elsewhere in these pyramids.

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The alternating letters A and N form the sides of the first pyramid. All the words in the second pyramid begin with A and end with AL.

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So far, we have concentrated on the first and last letters, the second and penultimate letters, and the first, penultimate and last letters. Now we turn our attention to the central letters of the words. As these central letters have to be arranged in a vertical line, each step of the pyramid adds two letters rather than the more normal one letter. The words of the first five pyramids below have one of the five major vowels as their central letter. The vowel in question does not occur elsewhere in the pyramid. …

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