Some of my earliest computer programming was done in 6502 assembly language. In most assembly languages there are a collection of instruction for rotating and shifting bits left and right in a byte (different instructions depending whether the carry bit is involved). Shifting to the left is the equivalent of multiplication by a power of two for each place, and to the right, dividing.
If, instead of bits, we used letters, and applied these operations to words, is it possible to make other words? A couple of lines of code later, and I had some examples.
Here’s an example on a ten letter solution (rotating the top two characters from the word on the left and adding them to the end):
A quick research of the internet did not reveal if these pairs of words have any special name, so I’ll make one up and call them rotagrams.
Rotagrams
I found a couple of thousand English language rotagram pairs. The longest pair being: EXPLOITATIONS and SEXPLOITATION at 13 letters.
A large number of the solutions involved rotating the ‘S’ off the end of a plural word, and moving it to the front to make the other word: TABLEMATES to STABLEMATE.
Also obvious were the compound words which were inverted to make other compound words eg. WORKBASKET to BASKETWORK, SHIPMASTER to MASTERSHIP, HOUSEBOAT to BOATHOUSE
The longest triplets I found were the words: RIPEST to STRIPE to TRIPES (six letters), and ABLEST to TABLES to STABLE (six letters).
There’s a quad with the words ESTOP to PESTO to STOPE to TOPES (five letters).
And finally, the following sets of three letter words are all perfect rotations: ASH to SHA to HAS, and CHI to HIC to ICH, and TEA to ETA to ATE, and ASK to SKA to KAS, and PAS to ASP to SPA, and ETH to THE to HET.
By definition, every two letter solution is a perfect rotagram if the letters switched make a new word! eg. NO to ON
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Solutions
Because it’s of no practical use to anyone, below is a list of all the solutions I found: