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        riddles >> hard >> Lowest Unattainable Number in Scrabble(tm)
        
(Message started by: ASB on May 26^th, 2004, 3:29pm)

Title: Lowest Unattainable Number in Scrabble(tm)
Post by ASB on May 26^th, 2004, 3:29pm

I have no idea what the solution to this is, but it occurred to me playing scrabble that it would be a somewhat interesting question to ask what the lowest number that could not possibly be a score for a single word in scrabble.
THe riddle can be posed in several ways: first given scrabble letter scoring and not assuming the outline of the board what is the first unattainable score (this may not simply be the score for the highest scoring word + 1 because the highest scoring word is not neccesarilly the successor to the second highest scorring word(s) etc.

A second and more challanging way to ask the riddle is to say given a scrabble board with double letter and tripple word placement etc. what is the first unattainable score.

A third way to make this even more challanging is to take instead of a blank board -- one in an ideal arrangement (you can arrange the board however you want before placing your word) and then ask what the lowest unattainable is.

To add even more complexity you could take a standard scrabble bag and ask given this distribution of letters what is the excpected lowest attainable.

letter values are as follows

A = 1; B = 2; C = 3; D = 2; E = 1; F = 4; G = 2; H = 4; I = 1; J = 8; K = 5; L = 1; M = 3; N = 1; O = 1; P = 3; Q = 10; R = 1; S = 1; T = 1; U = 1; V = 4; W = 4; X = 8; Y = 4; Z= 10; [blank] = 0;

http://www.moonatnoon.com/puzzles/reference/scrabful.gif

is a board -- pink is double word (ie total score of the word times two) Red is tripple word; Light Blue is double letter (value of the letter times two) and Dark Blue is Tripple letter (value of the letter times three).

Below is distribution and letter value table

Letter Value Count Letter Value Count
A 1 9 N 1 6
B 3 2 O 1 8
C 3 2 P 3 2
D 2 4 Q 10 1
E 1 12 R 1 6
F 4 2 S 1 4
G 2 3 T 1 6
H 4 2 U 1 4
I 1 9 V 4 2
J 8 1 W 4 2
K 5 1 X 8 1
L 1 4 Y 4 2
M 3 2 Z 10 1
[blank] 0 2

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by THUDandBLUNDER on May 26^th, 2004, 6:28pm

The lowest unattainable opening Scrabble score is.......1 ::) Otherwise....

The highest attainable opening play I could find is MUZJIKS. But I didn't have my board with me at the time.
(It's true!)
;)

MUZJIK: Russian peasant, especially prior to 1917 (Wordnet)

This scores 128.

Quote:

because the highest scoring word is not neccesarilly the successor to the second highest scorring word(s) etc.

CAZIQUE, JUKEBOX, and MEZQUIT all score 124.

Quote:

is a board -- pink is double word (ie total score of the word times two) Red is tripple word; Light Blue is double letter (value of the letter times two) and Dark Blue is Tripple letter (value of the letter times three).

Note that the above words all score much higher than would 'tripple', for example.

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Perfection on Jun 14^th, 2004, 10:13pm

No the highest obtainable is zxqkwwj for 168 (accounting for 50 point bingo bonus) Remember, the opponent doesn't have to challange you.

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by rmsgrey on Jun 15^th, 2004, 8:54am

That score is pathetic. With just 3 tiles (and a lot of help in advance) I can get a score (ignoring the other tiles involved) of more than 500 - assuming some dodgy words go unchallenged

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by towr on Jun 15^th, 2004, 12:14pm

not as an opening scrabble word (which is, I think, what he was talking about)

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Perfection on Jun 15^th, 2004, 7:17pm

Correct I was talking about an opening

The largest possible would be

WWZXVVJFFYYQHHK

Played accross the bottom it would score a whopping 2777!

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Perfection on Jun 15^th, 2004, 7:46pm

I have a hunch that the answer is 1mod(6) as it shouldn't be divisable by two or three (double and triple word scores) nor should it be equal to 2mod(3) because that could easily be done with a bingo on a triple.

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Nigel_Parsons on Jun 17^th, 2004, 10:55am

If we're talking about the opening move, then disregarding 1, (single letter words do not count!) the next lowest unobtainable scores are; ::[hide] 3, 5, 7, 9, etc.,
The rules require that the first word played must have one tile occupying the middle (double word) square.[/hide]::

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by rmsgrey on Jun 17^th, 2004, 1:17pm

OK, I should have realised from context that it was a first move score. And I apologise for the tone of my last post - some idiot had just dropped a computer monitor onto my foot so I wasn't in the best of moods...

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Three Hands on Jun 17^th, 2004, 5:12pm

You could still have one as an unobtainable value for the opening move, since you can have a three letter word, e.g. the, where two of the letters are blanks. However, it is possible, with the right set up, to score one for your turn at other times, by using blank tiles an an appropriate letter :)

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Perfection on Jun 18^th, 2004, 3:07pm

I've got it!

[hide]153 is the largest possible score without using any doubles triples or bingo bonuses is WZWVVXFFYJYHHQK played accross/down the 6th or 10th row/column. Any lower can also be created (Proving that to you would take too long but it is quite obvious that you can switch the 4s with 3s 2s or 1s and eventually create them all). So we know without doubles or triples anything from 0 (two blanks) to 153 can be created. Now with 50 point bingo bonuses we can show that anythng from 0 to 203 can be created (Bingos can be made on anything from 5 to 153 points) without double/triple bonuses. As shown before since 1mod(6) can't come from a double or triple the next number that satisfies it after 203 would be the lowest unattainable score that number is 205[/hide]

Now we dance!

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Perfection on Jun 18^th, 2004, 3:10pm

on 06/17/04 at 17:12:46, Three Hands wrote:

No, you open on a double word bonus so you can never get an odd value

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Three Hands on Jun 18^th, 2004, 5:29pm

on 06/18/04 at 15:10:30, Perfection wrote:

No, you open on a double word bonus so you can never get an odd value

Hence why I said it counts as an unobtainable value. I was merely stating that it was still a possible value while playing Scrabble, just not on the first turn, due to the double word score...although not particularly clearly, so apologies for that. Really shouldn't post so late at night - leads to less coherence :-/

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Perfection on Jun 19^th, 2004, 12:48am

Yeah, I see it now, sorry, I read it too fast.

Title: Re: Lowest Unattainable Number in Scrabble(tm)
Post by Nigel_Parsons on Jun 27^th, 2004, 6:09pm

"Perfection"'s answer above relies on an unchallenged word. Using no vowels, so the longest should be ::[hide]RHYTHMS[/hide]::.
Assuming "real" words are required, I'll start the ball rolling with words of 5 letters or less (thus playable with no bonus squares)
1,A (or 'an' using a blank, as single letters don't score)
2, An 3, Ant 4, And 5, Can 6, Cant
7, Cub 8, Cube 9, Off 10, Cake 11, Hake
12, Mix 13, Hex 14, Jive 15, Joke 16, Haze
17, Jack 18, Jacks 19, Hazy 20, Quack
Using a 'double letter score' for any capitalised letter (thus allowing 7 letter words with a middle letter doubled)
21, quAck 22 quiz 23 jacKs 24 Quid 25 sQuid
26 Quips 27 Query 28 Quarry 29, QuarRiEs (line either side of middle)

Take it from here!