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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"? $\endgroup$ – Rand al'Thor Mar 15 '15 at 18:23
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    $\begingroup$ "brushed" and "astride" seem good, but I have no idea if they're optimal. $\endgroup$ – Apple Mar 15 '15 at 19:50
  • $\begingroup$ Seems like programmers will defeat puzzlers again :( $\endgroup$ – ghosts_in_the_code Mar 16 '15 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. $\endgroup$ – Rand al'Thor Mar 16 '15 at 16:16
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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 Mar 16 '15 at 15:51
  • $\begingroup$ @Martin So? I don't see this mentioned anywhere in the problem statement... $\endgroup$ – dmg Mar 16 '15 at 16:14
  • $\begingroup$ the stetement reads "only uncapitalized words" $\endgroup$ – Alexis Mar 18 '15 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 Mar 19 '15 at 8:26
  • $\begingroup$ "cacafugo" is not in Merriam Webster, but "cacafuego" is. $\endgroup$ – Alexis Mar 19 '15 at 15:43

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