A Sobering Problem

Anything goes, but keep it seemly...

Re: A Sobering Problem

Postby David P Bird » Fri Sep 13, 2013 8:44 am

Leren, very clever!

Rather humbling to find you nearly halved my path and then, to add insult to injury, were able to extend it!

David
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England

Re: A Sobering Problem

Postby Leren » Fri Sep 13, 2013 12:00 pm

I'm still not sure I've answered JPF's question correctly. If the question is to be interpreted as:

How far can we go from a "mouse" ? Then maybe the correct answer is:

Code: Select all
  mouse

1 mousy
2 mossy
3 mosey
4 cosey
5 coset
6 comet

Too much Sudoku makes one logical, not reasonable :lol:

Leren
Leren
 
Posts: 2928
Joined: 03 June 2012

Re: A Sobering Problem

Postby JPF » Fri Sep 13, 2013 12:44 pm

well, you can go even further:

Code: Select all
     mouse
1    mousy
2    mossy
3    missy
4    misty
5    mists
6    gists
7    gests
8    gents
9    genus
10   venus

but your first answer was correct.
Here is my new proposal:
Code: Select all
     mouse
1    morse
2    morae
3    moras
4    molas
5    molar
6    solar
7    sowar
8    sewar
9    dewar
10   debar
11   kebar
12   kabar
13   kabab
14   kabob
15   nabob

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Re: A Sobering Problem

Postby Leren » Fri Sep 13, 2013 9:20 pm

Code: Select all
     mouse
1    morse
2    morae
3    moras
4    molas
5    molar
6    solar
7    sowar
8    sewar
9    dewar
10   debar
11   kebar
12   kabar
13   kabab
14   kabob
15   cabob
16   carob

On the astronomical front

Code: Select all
  mouse
1 morse
2 morae
3 moras
4 monas
5 nonas
6 novas

Leren
Leren
 
Posts: 2928
Joined: 03 June 2012

Re: A Sobering Problem

Postby JPF » Sat Sep 14, 2013 10:20 am

Code: Select all
     mouse
1    morse
2    morae
3    moras
4    molas
5    molar
6    solar
7    sowar
8    sewar
9    dewar
10   debar
11   kebar
12   kabar
13   kabab
14   kabob
15   cabob
16   carob
17   carol
18   parol


parol is also a star ; see here

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Re: A Sobering Problem

Postby JPF » Thu Sep 19, 2013 10:07 am

Now try getting from seven to eight.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Re: A Sobering Problem

Postby Leren » Thu Sep 19, 2013 11:28 am

Code: Select all
    seven
1   sever
2   saver
3   saner
4   sanes
5   sines
6   sinhs
7   sighs
8   sight
9   eight

Leren
Leren
 
Posts: 2928
Joined: 03 June 2012

Re: A Sobering Problem

Postby Smythe Dakota » Fri Sep 20, 2013 3:33 am

Try getting from one palindrome to another, with all the intermediate steps also palindromes. Of course, you must change two letters on each turn, unless the letter you change is the middle one.

Bill Smythe
Smythe Dakota
 
Posts: 534
Joined: 11 February 2006

Re: A Sobering Problem

Postby JPF » Fri Sep 20, 2013 9:18 am

Leren wrote:
Code: Select all
    seven
1   sever
2   saver
3   saner
4   sanes
5   sines
6   sinhs
7   sighs
8   sight
9   eight


Here are some variations:
Code: Select all
  seven   seven   seven   seven   seven   seven
1 semen   semen   sever   sever   sever   sever
2 semes   semes   saver   serer   siver   siver
3 seres   sexes   saves   seres   siker   sizer
4 sires   sixes   sanes   sires   sikes   sizes
5 sines   sines   sines   sines   sines   sines
6 sinhs   sinhs   sinhs   sinhs   sinhs   sinhs
7 sighs   sighs   sighs   sighs   sighs   sighs
8 sight   sight   sight   sight   sight   sight
9 eight   eight   eight   eight   eight   eight

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Re: A Sobering Problem

Postby Leren » Fri Sep 20, 2013 9:44 pm

Smythe Dakota wrote:Try getting from one palindrome to another, with all the intermediate steps also palindromes. Of course, you must change two letters on each turn, unless the letter you change is the middle one.

Bill Smythe

I assume you mean to produce the longest continuous sequence of palindromes with the same number of letters. One approach is to use Scrabble 3 letter palindromes. I came up with the following sequence of 40 words starting and ending with a consonant:

GAG GIG BIB BOB BUB DUD DAD DOD DID SIS SUS SOS WOW WAW YAY VAV HAH HEH HOH HUH MUM MAM MEM MIM MOM TOT TET TIT TUT TAT NAN NUN NON POP PEP PIP PAP PUP ZUZ ZZZ

I also came up with a list of 22 Scrabble 3 letter palindromes starting and ending with a vowel:

EKE EME ENE ERE EVE EYE EWE AWA AIA AKA ALA ABA AGA AMA AVA ANA AUA AHA OHO OBO ONO OXO

Leren

<Edit> Extended consonant list to 40 words by adding DOD, HOH, MAM, NON, SUS & ZZZ and rearranging. Extended vowel list to 22 words by adding ANA, AIA, AKA, AUA, ENE & OBO.

OHO OBO OXO ONO ENE EKE EME ERE EVE EYE EWE AWA AKA ALA ULU UTU UMU AMA ABA AGA AVA ANA AUA AHA AIA MIM MUM MEM MOM MAM GAG GIG BIB BOB BUB DUD DAD DOD DID SIS SUS SOS WOW WAW YAY VAV HAH HEH HOH HUH TUT TOT TET TIT TAT NAN NUN NON POP PEP PIP PAP PUP ZUZ ZZZ ZIZ

<Edit> Managed to combine the consonant and vowel lists into a combined list and added ZIZ for a total of 63 words. Added ULU, UTU & UMU and rearranged a bit for a total of 66 words.
Leren
 
Posts: 2928
Joined: 03 June 2012

Re: A Sobering Problem

Postby Smythe Dakota » Sun Sep 22, 2013 5:54 am

It appears that you can get from any 3-letter palindrome to any other via legal English-language palindromes.

Is the same true for 5 letters?

Bill Smythe
Smythe Dakota
 
Posts: 534
Joined: 11 February 2006

Re: A Sobering Problem

Postby Leren » Sun Sep 22, 2013 11:08 am

Smythe Dakota wrote:It appears that you can get from any 3-letter palindrome to any other via legal English-language palindromes.

Is the same true for 5 letters?

Bill Smythe

2 letters

4 palindromes - longest sequence 4

aa ee mm oo

4 letters

18 palindromes

abba
acca
anna – an Indian coin
boob – a blunder; a breast
deed – various common meanings
ecce
esse – existence or essence
goog – an egg (Australian slang)
keek – to peep
kook – a crazy person
naan – a type of Indian bread
noon – midday
oppo
otto – variant of attar, an essential oil
peep – various common meanings
poop – a raised deck at the stern of a ship; various other meanings
sees – third-person present tense of ‘to see’
toot – the sound made by a horn or whistle

3 sequences covering all 18

oppo otto || abba acca anna ecce esse || sees deed peep keek kook toot poop goog boob noon naan

6 letters

12 palindromes

degged - past tense of to deg, meaning to water a plant
denned – past tense of to den, meaning to live in a den
hallah – a variant of challah, a type of bread traditionally eaten by Jews
mallam – in West Africa, a learned man
marram – a type of grass
pullup – an exercise in which one pulls oneself up by the arms
redder – more red
selles – plural of selle, an archaic word for a saddle
sesses – plural or third-person present tense of sess, an archaic word for tax (a variant of assess)
succus – any of various liquids excreted by animals or plants
terret – a metal ring on a harness, through which the reins pass
tirrit – according to Webster’s Dictionary (1913): "A word from the vocabulary of Mrs. Quickly, the hostess in Shakespeare’s Henry IV., probably meaning terror"

Longest sequence I can see - 3 hallah mallam marram

Leren
Leren
 
Posts: 2928
Joined: 03 June 2012

Re: A Sobering Problem

Postby JPF » Thu Sep 26, 2013 1:34 pm

We can define a distance d between two words word1 and word2:

d (word1, word2) = minimum number of steps necessary to go from word1 to word 2.

Some words are not connected ; then we can say d (word1, word2) = infinity

In the set of five-letter words, what is the greatest finite distance? Give an example.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Re: A Sobering Problem

Postby David P Bird » Fri Sep 27, 2013 8:29 am

This suggests a two-player game:
THe first player starts with a 4 or 5 letter word (which mustn't be a dead end).
Players then alternate changing one letter at a time to produce a new word that doesn't repeat a previous one.
The loser is the player that can't continue the chain.

So, are there any words that guarantee a win for the first player?

Please consider me a spectator, not a player, as I wouldn't stand a chance in the present company!
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England

Re: A Sobering Problem

Postby JPF » Fri Sep 27, 2013 5:38 pm

David P Bird wrote:So, are there any words that guarantee a win for the first player?

Yes, here are two examples:
Code: Select all
demur
femur
lemur

Code: Select all
enjoy
envoy
envoi

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

PreviousNext

Return to Coffee bar