465 word pairs might allow the construction of a much more interesting set of word-bounded palindromic sentences!!

I wonder whether we can assign fractional values to pairs that use iffy words. Perhaps an algorithm can be derived from the results of a Google search to assign a reasonable fractional value of properness to any word.

]]>Using /usr/share/dict/web2 on my macbook, I get 465 pairs.

Some pairs are quite obscure, e.g. diorama/amaroid. On the other hand, leveler/relevel seems proper.

]]>By the way, apres, reaps, rapes, spear, pears, pares, spare, parse, and prase are all anagrams of each other, so there are a few interesting cases out there.

]]>pots

pits

spot

stop

tips

tops

prepend each word with the string you get from sorting its letters and then sort the list by the first column to get:

ipst pits

ipst tips

opst pots

opst spot

opst stop

opst tops

The groups of repeated lines (by first column) will give you the words that are anagrams of one another. That works, doesn’t it?

]]>The number of different words you might get by permutation is far larger. Consider a word as a string of letters:

A

where each superscript denotes the number of times that letter is repeated.

The number of unique permutations of that string of letters is:

(i+j+k…)! / (i! j! k! …)

That factorial in the numerator is going to grow a lot faster than anything happening in the denominator. For most words the number of letter combinations to include in the search is going to be a really large number.

]]>Incidentally, try a Google search for “anagram”. I never saw that one before ðŸ™‚

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