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        riddles >> easy >> Word Ladder II
        
(Message started by: TenaliRaman on Jun 29^th, 2003, 3:34am)

Title: Word Ladder II
Post by TenaliRaman on Jun 29^th, 2003, 3:34am

(Inspired by the other topic of Word Ladder)

Are there three words W1,W2 and W3 such that W1 transforms to W2 and W2 transforms to W3 and W3 transforms to W1??

i have been trying to find these but alas my efforts are in vain.

Title: Re: Word Ladder II
Post by BNC on Jun 29^th, 2003, 4:45am

I think you should place some limitations on W1,W2,W3. Otherwise, you could use words like butter-bitter-better.

Title: Re: Word Ladder II
Post by Sir Col on Jun 29^th, 2003, 6:02am

I don't think this will really work, TenaliRaman, at least not with three words.

As BNC has pointed out you could just change, say, the first letter of a word: GUN, FUN, BUN.

However, if you insist that the same letter cannot be changed more than once, it will be impossible to get back to W1, as you will need to change two letters in one move. For example, ACE, ACT, APT; you would need to change P and T to get back to ACE.

If you tried the same thing with four words, insisting that you could only change one letter position at most twice and you may not repeat a word, it will work.

An workable example can be found by extending the example above: ACE, ACT, APT, APE.

It might be interesting to ask...

Having found a set of four 3-letter words, can you find a set of 4-letter, 5-letter words? What is the longest letter set you can find?

Can you find a set of five words that have this property?

Title: Re: Word Ladder II
Post by THUDandBLUNDER on Jun 29^th, 2003, 6:40am

I assume they must have no letters in common. But how about word length?

: [hide]
AN
at
IT
if
OF
on
AN
[/hide]:

Title: Re: Word Ladder II
Post by TenaliRaman on Jun 29^th, 2003, 7:12am

T&B got what i was thinking about.

i found one more example,
HEAT to WARM to COLD to HEAT

[Hide]HEAT --> heft --> haft --> hart --> wart --> WARM --> ward --> card --> care --> core --> cord --> COLD --> bold --> bolt --> boat --> beat --> HEAT[/Hide]

/*ofcourse i forgot to mention that none of the links are to be shared.*/

Sir Col's question though is interesting.... i will try and check into it as soon as i get time soon.

Title: Re: Word Ladder II
Post by tohuvabohu on Jun 29^th, 2003, 9:49am

How about this for a challenging triple ladderword: a closed loop of 12 four-letter words, in which no word has any letters in common with any word more than three steps away from it. You can start anywhere in the loop, and the first, fourth, and eighth words will be completely different.
I have one solution I'll post later on.

Title: Re: Word Ladder II
Post by Sir Col on Jun 29^th, 2003, 11:19am

I expect you meant, "the first, fifth, and ninth words will be completely different," tohuvabohu? As you can't change four letters by the time you get to the fourth word.

This is an excellent, albeit very hard, puzzle.

To make things even more difficult (like it needs to be), once you've solved tohuvabohu's puzzle, can you find a twelve 4-letter word loop, such that the 1st, 2nd, 3rd, 4th letters are changing in a continuous loop?

For example,
HARD HERD HEAD HEAT
FEAT FIAT FIST FISH
WISH WASH (WARH) WARD

This doesn't work, because WARH is not a word.

Does one exist? ???

Title: Re: Word Ladder II
Post by tohuvabohu on Jun 29^th, 2003, 2:12pm

No, actually I meant the 0th, 4th, and 8th. (That way I only made one mistake).
Here's one solution with the letters changing in order:
[hide]The 0th, 4th, and 8th words are
TIME...BALK...DUNS
[/hide]

Title: Re: Word Ladder II
Post by Sir Col on Jun 29^th, 2003, 2:46pm

on 06/29/03 at 14:12:41, tohuvabohu wrote:

No, actually I meant the 0th, 4th, and 8th. (That way I only made one mistake).[/hide]

:P to you too!

That twelve word loop solution is very inspired, tohuvabohu. I am truly impressed. 8)

Title: Re: Word Ladder II
Post by TenaliRaman on Jun 29^th, 2003, 4:01pm

One more twelve word loop
[hide]
MICE --> mite --> rite --> rate --> RATS
RATS --> rots --> cots --> cons --> CONK
CONK --> monk --> mink --> mine --> MICE
[/Hide]