Justin Li


Circular Logic - "glow"

2011-04-04

The NYTimes has a regular column on math puzzles. I don't usually look at them, but when I do I prefer Dos Equis... what? Oh yes, Numberplay. Most of the time I can't be bothered to figure out the answer, but one of the questions this week happens to be computationally easy. The question is:

Consider the word "glow." If you replace each letter with its counterpart in a mirror alphabet you will get the legitimate word "told." What other words exhibit this same property?

So I started wrote a little script in Python:

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#!/usr/bin/env python3import reif __name__ == "__main__":    src = open("/usr/share/dict/cracklib-small", "r")    words = set()    for word in src:        word = word.strip()        if len(word) == 1 or re.match('[^a-z]', word):            continue        words.add(word)    src.close()    for word in words:        mirror = "".join(chr(219-ord(c)) for c in word)        if mirror in words:            print(word, mirror)

This script uses the computer's dictionary file (which I've used before), mutates the letters, then checks if the result is in the dictionary. The script outputs:

all   zooark   zipart   zigblip  yorkde    wvdr    widrib  wiryelm   vonera   vizerr   viifir   urifm    unge    tvgirl  triogirt  trigglib  toryglow  toldgm    tngs    thhob   slyhold  slowholt  slogholy  slobhorn  slimir    riirk   ripiv    reivy   reblevi  overlow   oldlug   oftmd    nwme    nvmix   nrcmn    nmmrs   nihms    nhnh    msnih   mrsnm    mnnrc   mixnv    menw    mdoft   lugold   lowover  levire    ivreb   ivyri    irrip   irkslim  hornslob  holyslog  holtslow  holdsly   hobth    gstn    gmtold  glowtory  glibtrig  girttrio  girltv    geun    fmuri   firvii   errviz   eravon   elmwi    drwiry  dribwv    deyork  blipzig   artzip   arkzoo   all

As a sanity check, notice that "glow" does indeed turn into "told" (and vice versa).

Problem solved in 10 minutes.

PS. I would have commented on the post, but I have no clue what my NYTimes password is.

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