Assign the values of 1 through 26 respectively to A through Z.

Find words of x letters (all letters and words¹ different) such that the sum of letter values becomes the word value that fits each table category.

The table values represent the best values, being the lowest and highest, for which I was able; the left column represents word length. Can you also do better by providing a word lower or higher than the table value?

The blank cells are for those who wish to press this further.

			Prime		Triangle		Square
			Lowest	Highest	Lowest	Highest	Lowest	Highest
		3	7	61	6	66	9	64
		4	13	79	15	78	16	64
		5	19	89	21	91	36	81
		6	37	109	36	91	49	100
		7	47	97	66	78	81	100
		8
		9

¹Special note: Should a word score 36 (being both a triangle and square) neither a repetition of it nor any anagrams is considered acceptable.

(In reply to re: computer solution by Dej Mar)

Without repeating letters within words:

bad vox    cab wry    ace sty    
aced putz    cafe onyx    cage wyns    
badge rusty    abide fusty    clade aunty    
bached frowzy    abduce dyvour    abduce bronzy    
dogface poultry    bighead nostrum    bighead poverty    
blockade quixotry    backfire mugworts    beaching poxvirus    
backfield nervously    backslide curtsying    abducting autolyzes    
boldfacing hypnotizes    blockading grievously    candlefish formulizes    
becowarding vexatiously    disgraceful countryside    cabinetwork unseaworthy    
descrambling outsparkling    flowcharting housewarming    counterplays counterplays    
unproblematic metalworkings     .  .     .  .    
troublemakings troublemakings     .  .     .  .    

 

Stats:

 3   7  61      3   6  66      3   9  64
 4  13  83      4  15  78      4  16  81
 5  19 103      5  21  91      5  25  81
 6  23 113      6  36 105      6  36 100
 7  41 127      7  36 120      7  36 121
 8  53 149      8  55 136      8  49 144
 9  53 151      9  66 136      9  81 144
10  73 157     10  78 153     10  81 144
11 101 173     11 105 153     11 121 169
12 107 163     12 136 153     12 169 169
13 149 167     
14 167 167 

For one of the abduce's, substitute one of the following:

barfed
becalm
calked
cohead
facile
fecial
lacked

I don't have a substitute for any bighead.

Edited on March 1, 2009, 4:09 am

Posted by Charlie on 2009-03-01 04:01:34