Foldedness Factor In Letter Arrays

An idle diversion with pencil and graph paper involves writing some ordered sequence of letters in the cells of a grid and searching the horizontal, vertical and diagonal rows of the resulting array for accidentally-formed new words. Since there is usually a multiplicity of possible ways to inscribe a given letter string into a grid, the question arises as to whether some inscription patterns are likely to be more productive of new words than others. Logic suggests that the answer is yes. Because any new words in the array must form along straight lines, and because no answer is yes. Because any new words in the array must form along straight lines, and because no new words can form entirely within the line of the original letter sequence, grid space that is occupied by straight-line segments of that sequence is partly unavailable for new-word formation. Ergo, those inscription patterns that break or fold the original letter string into the shortest straight-line segments presumably offer the greatest opportunity for new words to form