11
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Inspired by this great question by Uvc (actually, it's the same logic but with different words).

How fast one can get from EIGHT to SEVEN?

The rules are the same:

  • You are only allowed to change one letter at a time.
  • You have to keep the word length the same.
  • At each step of the way, you must have a legitimate English word. Thus, something like going from "EIGHT" to "EIGHN" is not a valid step, but from "FIGHT" to "NIGHT" would be.

Here is an example 11-step way (but with very obscure words involved): eight-sight-sighs-sikhs-sikas-simas-simar-sizar-sizer-siver-sever-seven.

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    $\begingroup$ If you want more there are other similar puzzles: Turn Lead into GOLD, Lead into Iron, Really? , Want to go from HAVANA to MANILA. Check them out $\endgroup$ – DEEM Jun 11 at 12:18
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Here's my 8-step solution:

EIGHT SIGHT SIGHS SINHS SINES SENES SEMES SEMEN SEVEN

(I don't know if SINHS - plural for SINH ("hyperbolic sine function") is an accepted word)

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    $\begingroup$ It is interesting how FIVE->FOUR requires five steps and EIGHT->SEVEN requires eight steps ... $\endgroup$ – TheSimpliFire Jun 11 at 8:21
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    $\begingroup$ I really don't think you can pluralize "sinh" as an abbreviation for "hyperbolic sine"; at any rate I don't think I've ever seen it done. But a sinh also turns out to be a kind of Thai clothing, and it seems OK to pluralize that :-). $\endgroup$ – Gareth McCaughan Jun 11 at 12:04
  • $\begingroup$ @GarethMcCaughan "The variables $x,y,z$ are all positive and therefore so are their sinhs." $\endgroup$ – Rand al'Thor Jun 11 at 13:29
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    $\begingroup$ Yeah, see, I'd never ever write that. I'd write "and therefore so are their hyperbolic sines", or "and therefore so are $\sinh x,\sinh y,\sinh z$", or "and therefore so are the results of applying $\sinh$ to them", or something. $\endgroup$ – Gareth McCaughan Jun 11 at 14:22
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Six steps - Shameless use of Old English with Wiktionary support:

Eight > light > liget > ligen > liven > leven > seven

Ten steps - If you insist on using Modern English, here is a shortened one highly based on @Gareth's:

eight bight bigot begot beget beset reset revet rever sever seven

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  • $\begingroup$ (+1) I think this is the minimum. Five steps implies that each letter of eight must be directly changed to the corresponding one of seven which can be proved to be impossible. $\endgroup$ – TheSimpliFire Jun 11 at 8:29
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    $\begingroup$ Those are not English words. (Old English is a different language, as different from English as Latin is from Italian.) $\endgroup$ – Gareth McCaughan Jun 11 at 12:02
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    $\begingroup$ @TheSimpliFire Exactly, for a 5-step solution, the first step is EIGHT → SIGHT (as EEGHT, EIVHT, EIVET and EIGHN don't exist), and there's no possible second step, since none of SEGHT, SIVHT, SIGET or SIGHN exist. $\endgroup$ – EKons Jun 11 at 18:23
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Eight step solution

Eight - Bight - Bigot - Begot - Begat - Bevat - Bevan - Beven - Seven

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    $\begingroup$ in my humble opinion, names and proper nouns are a bit of a stretch as we can all make up names... $\endgroup$ – Omega Krypton Jun 11 at 9:44
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    $\begingroup$ Thanks @OmegaKrypton what shall I do now ? $\endgroup$ – Ak19 Jun 11 at 9:48
  • $\begingroup$ it's up to you - maybe you can try to lessen the dependence on proper nouns? $\endgroup$ – Omega Krypton Jun 11 at 9:54
  • $\begingroup$ Thanks @OmegaKrypton I've deleted the last two - which contained names :) $\endgroup$ – Ak19 Jun 11 at 9:59
  • $\begingroup$ Is your fifth step only a Dutch word, or is it also known in Englsh ? $\endgroup$ – Evargalo Jun 11 at 12:11
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This is longer (12 steps) than the other solutions here but uses only words I can actually define (and that aren't proper nouns or words only in other languages like "Old English" which despite the name really shouldn't be considered the same language as English). Anyone got a shorter ordinary-words-only solution?

eight bight bigot begot beget beset reset revet revel level lever sever seven

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  • $\begingroup$ Two steps from RIGHT to RIVET would shorten this, but is alas impossible. $\endgroup$ – Rand al'Thor Jun 11 at 13:13
  • $\begingroup$ Indeed. The route away from -GHT is pretty narrow. $\endgroup$ – Gareth McCaughan Jun 11 at 13:19
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Without using somewhat obscure words, there is no way to go from EIGHT to SEVEN.

(12 steps) with one rare word (the same as what @Gareth McCaughan got):

eight bight bigot begot beget beset reset revet revel level lever sever seven

The rarish word is asterisked. To find this I used a program which knows the rarity of each word (via the SCOWL word list)

(11 steps) allowing rare English words (rare words asterisked):

eight bight bigot begot beget benet* benes* nenes* neves* never sever seven

Allowing removal of letters, we have:

(9 steps) preferring common words:

eight sight sigh sign sin kin ken keen seen seven

(7 steps) shortest possible including rare words:

eight sight sigh sign sin sen* seen seven

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