The Complete Tw12ve (Unpub)

Numbers may be communicated in the form of 

expressions -- written or spoken -- using numerals 

('1,' '3.1416...,' '4 + 4,' etc.) and in the form of 

words ('one,' 'three point one four one six,' four plus 

four,' etc.). 

The following observations are made with reference 

to expressions in the form of words.

Among whole numbers from zero through twelve, 

four of them may be expressed as three-letter words: 

     ’one,’ ‘two,’ ‘six’ and ‘ten.' 

In addition, ‘and,’ a so-called function word, is also 

a three-letter word. 

Thus there are a total of five three-letter words. 

Also among the set of whole numbers expressed as

words are four four-letter words:

 

     ’four,’ ’five,’ ‘nine’ and ‘zero.' 

In addition, ‘plus,’ a function word, is a four-letter 

word. 

Thus there are a total of five four-letter words. 

(We disregard the symbol '+' as being, strictly 

speaking, neither a word nor a numeral.) 

Further, there are among that set three five-letter 

words: 

     ‘three,’ ‘seven,’ and ‘eight.'

 

Moreover, ‘minus,’ a function word, is a five-letter 

word. 

Thus there are four five-letter words. (The symbol '-' 

is disregarded similarly as per the symbol '+' above.) 

Finally, among that set there are two six-letter words: 

     ‘eleven’ and ‘twelve.’

To summarize:

five three-letter words: 

     'one,' 'two,' 'six,' 'ten,' (plus 'and' )
five four-letter words: 

     'four,' 'five,' 'nine,' ('plus' and 'zero') 
four five-letter words: 

     'three,' 'seven,' 'eight,' (plus 'minus') 
two six-letter words: 

     'eleven,' (plus 'twelve')          

Note that several of these 16 words appear between 

parentheses in the above list. This is because none of 

the expressions observed below is constructed using 

any of the words so appearing. It is with reference to 

expressions formed from combinations of only 11 words, 

therefore (i.e., those words not in parentheses) -- four 

three-letter words, three four-letter words, three 

five-letter words and one six-letter word -- that the 

observations are made.

These 11 words, i.e., the words designating the whole 

numbers between 0 and 12 -- excepting 0 and 12 -- 

plus 'and,' can be combined in various ways to yield a 

series of 12-letter expressions (not counting spaces 

between words or implicit punctuation) of which the 

numerical value is 12.

 
     E.g., ‘one, one and ten’ is such an expression, the 

words of which contain a total of 12 letters and the 

value of which, expressed in numerals, is 12. 

So is the expression ‘eight and four,' and so forth. 

So far, 22 such expressions have been constructed. 

11 of them – precisely one half of the number of 

expressions constructed and a total identical with 

the count of number words drawn upon -- employ 

the word 'and'; precisely 11 of them do not. 

Here they appear in a simple array (fig. 1):

O N E O N E AN D T E N
O N E T E N A N D ON E
O N E F O U R S E V E N
O N E S E V E N F O U R
O N E A N D E L E V E N
TWO  TWO  TWO  S I X
T WO T WO S I X T WO
T WO S I X T WO T WO

T H R E E A N D N I N E
F O U R O N E S E V E N
F O U R FO U R F O U R
F O U R S E V E N O N E
F O U R A N D E I G H T
F I  V E A N D S E V E N
S I X T WO T WO T WO
S E V E N A N D F  I V E
S E V E N O N E F O U R
S E V E N F O U R O N E 
E I G H T A N D F O U R
N I  N E A N D T H R E E
T E N O N E AN D O N E
E L E V E N A N D O N E

          (fig. 1) 

*   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   

                                          E I G H T A N D F O U R
                     F O U R A N D E I G H T 
                                       T E N O N E A N D O N E
                              O N E T E N A N D O N E 
            O N E O N E A N D T E N                              
                                  S E V E N F O U R O N E
                                  S E V E N O N E F O U R 
                                  S E V E N A N D F I V E 
                         O N E S E V E N F O U R 
                      F O U R S E V E N O N E 
             F O U R O N E S E V E N 
              F I V E A N D S E V E N 
            O N E F  O U R S E V E N                            
                                E L E V E N A N D O N E 
             O N E A N D E L E V E N 
                                  N I N E A N D T H R E E  
          T H R E E A N D N I N E

 
                         T W O T W O T W O S I X 
                          S  I X T W O T W O T W O
                 T W O S I X T W O T W O
       T W O T W O S I X T W O                                      
                                       F O U R F O U R F O U R

 
                                     (fig. 2) 

 
                E I G H T A N D F O U R
                                        F O U R A N D E I G H T
                                 T E N O N E A N D O N E
                                           O N E T E N A N D O N E
                                           O N E O N E A N D T E N
                        S E V E N F O U R O N E
                          S E V E N O N E F O U R  
                                          O N E S E V E N F O U R
                                       F O U R S E V E N O N E
                                       F O U R O N E S E V E N
                                          O N E F O U R S E V E N
               E L E V E N A N D O N E
                                           O N E A N D E L E V E N

                                   T W O T WO T W O S I X
                           S I X T W O T W O T W O
                                   T W O S I X T W O T W O
                                   T W O T W O S I X T W O
                                       F O U R F O U R F O U R
 
                                 N I N E A N D T H R E E
                                 T H R E E A N D N I N E
                                  F I V E A N D S E V E N 
                                 S E V E N A N D F I V E

                                              (fig. 3)

All but five expressions include 'e,'; all but five include 

'n,' and all but four include 'e,' as the figs above show.

Not the least interesting aspect of this phenomenon, 

of course, regardless of the manner in which its elements 

are arrayed, is the fact of its random character. That 

these word combinations can be assembled to yield the 

value of 12 is based largely on the chance circumstances 

of their containing the number of letters they do and the

way they are spelled. Obviously the same condition would 

not obtain, or would do so in some different manner, using 

number words from languages other than American English.

                                                                             
* *  *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *

To create 3x4-letter blocks, the 12 letters of each expression 

above may be ordered in various ways -- left-to-right, right-

to-left, alternate (beginning from either end), top-to-bottom, 

inward- or outward-turning spirals beginning at different loci, 

and so forth. 

Inserting the letters in order left to right into four-letter rows 

and stacking these rows three-deep, top to bottom, results 

in blocks as in the following figures:

>  O N E O            >    E I GH
>  N E A N            >    T A ND

>  D T E N            >     F OUR          etc.

The 22 blocks so constructed may be variously arrayed, 

these different arrays possessing various kinds of 

symmetry. 

One possible array, shown below...