Sunday, April 16

Words from numbers

Last week I presented a "word" continuation puzzle. The algorithm used to create the list isn't too difficult to discover, applying English number words (one, two, three, ...) to the previous term (the zeroth assumed to be an empty string). Thus, one letter at a time, the second term from the first:

one +two
onet
onetw
netw

A letter gets added to the right if it doesn't already exist in the evolving string. It is deleted from the string if it does already exist. Thus the string will never contain more than one copy of any particular letter. If you noticed the double-comma near the end of my puzzle, that wasn't a typo: ourihten +onehundrednineteen results in an empty string, which +onehundredtwenty yields ohurweny, which +onehundredtwentyone yields one. Using Mathematica's built-in dictionary and ignoring already encountered words (such as one at index 121), here is a list of English found in a deep continuation:

         1 one
     21240 visaed
     45660 fads
     57242 ado
    155868 woad
    171524 aide
    271966 ad
    337664 waned
    347660 audit
    413700 and
    423066 roads
    507504 wained
    537056 goads
    557924 aid
    615808 wad
    619808 wade
    635830 wand
   1152766 mad
   1250766 moaned
   1272524 maid
   1298168 made
   2710904 maned
   3526644 mashed
  10984236 mawed
  16170624 maiden
  21730304 mated
  67092006 mead
 509056060 remands
 540798800 moated
1000080796 boards
1000146526 bards
1000152766 bad
1000298168 bade
1000530740 baud
1000558076 broads
1000562062 brands
1000748080 bandit
1000750040 band
1000816952 bandy
2000710904 baned
...

Why would all of our subsequent English dictionary words appear at even indices?

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