Magazine article Word Ways

Invertible Word Squares and Rectangles

Magazine article Word Ways

Invertible Word Squares and Rectangles

Article excerpt

Clap in his walie nieve a blade, he'll make it whissle, An' legs an' arms an' head will sned, like taps o' thrissle.

--from Robert Burns, "Address to a Haggis"

Eric Harshbarger recently posed an interesting question: what are the largest word squares or rectangles that can be found which transform into another, valid, word square or rectangle when turned upside down? In order to investigate this question, one must decide on an invertible font, in which as many letters of the alphabet as possible also form a letter of the alphabet (ideally a different one, but perhaps the same) when inverted. Combining some of my ideas with some of Eric's, I settled on the font shown below.


Here each glyph is shown above its upside-down version, and every letter inverts into a valid letter with the exception of "c". Like malay ambigrammatic fonts this one is not perfect. The most dodgy letter is the v/r glyph; I decided to allow it because it turns out to be a fruitful one for forming invertible word rectangles, as will become apparent from the lists below. I wasn't completely happy with including some upper-case letters (the invertible N and the K/H pair) in a predominantly lowercase font, but again these turned out to be quite useful.

For the list of valid words I used the latest version of the Scrabble Official Tournament and Club Word List (TWL06). I decided to consider only those squares and rectangles that are dense, which means that all N+M words in its NxM grid are different. An invertible NxM grid is said to be invertibly dense if the 2N+2M words in the original and inverted grids are all different. …

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