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When I write text messages on my mobile phone I just need to press each key once for each letter and it automatically finds the most likely word that fits the combination (abc=2, def=3, ghi=4, jkl=5, mno=6, pqrs=7, tuv=8, wxyz=9). So if I press 84373 it displays "there", although the word could as well be "these".

What is the longest pair of English words that have the same number combination, while having no common letter in the same position?

Note: The words must occur in the Merriam Webster dictionary; only uncapitalized words; no hyphens.

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  • $\begingroup$ Can you define "common letter"? $\endgroup$ Commented Mar 15, 2015 at 18:23
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    $\begingroup$ "brushed" and "astride" seem good, but I have no idea if they're optimal. $\endgroup$
    – Apple
    Commented Mar 15, 2015 at 19:50
  • $\begingroup$ Seems like programmers will defeat puzzlers again :( $\endgroup$ Commented Mar 16, 2015 at 10:18
  • $\begingroup$ @Gamow You're right about "open-ended", sorry! I was thinking this was much like the other "open-ended" puzzles involving "find the longest dictionary word such that...", but this one is different because it specifies a (searchable) dictionary. $\endgroup$ Commented Mar 16, 2015 at 16:16

2 Answers 2

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278-7433: astride and brushed
266-8687: amounts and contour
468-2337: hotbeds and invader

These seem to be the longest pairs that don't share a letter in the same place. If you allow letters in the same place, there is a 10-letter pair, including area code:

(732)773-7833: rearrested and reasserted.

These seem to be the longest pairs, and it's a coincidence it's the same length as a phone number.

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The answer is:

8. Two pairs achieve this length: jingling and khoikhoi translated as 54645464, as well as acacetin and cacafugo translated as 22223846

Why?

Brute-forced on a dictionary.

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  • $\begingroup$ But "Khoikhoi" is capitalized. $\endgroup$
    – Alexis
    Commented Mar 16, 2015 at 15:51
  • $\begingroup$ @Martin So? I don't see this mentioned anywhere in the problem statement... $\endgroup$
    – dmg
    Commented Mar 16, 2015 at 16:14
  • $\begingroup$ the stetement reads "only uncapitalized words" $\endgroup$
    – Alexis
    Commented Mar 18, 2015 at 16:39
  • $\begingroup$ @Martin I did not notice that. Either way, the other pair is correct, so I see no reason for downvotes. $\endgroup$
    – dmg
    Commented Mar 19, 2015 at 8:26
  • $\begingroup$ "cacafugo" is not in Merriam Webster, but "cacafuego" is. $\endgroup$
    – Alexis
    Commented Mar 19, 2015 at 15:43

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