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.

Charlie's computer-assisted assembled word list appears to be composed of the first word alphabetically that fits the condition of lowest or highest score. Many of the words offered by Charlie bested those that I had discovered, yet I did find solutions to a few of equal score that were not at the beginning of the alphabetical offering. For instance, in addition to the four-letter low prime [13] aced are its anagrams cade and dace; in addition to the four-letter high prime [83] putz is the word towy; in addition to the five-letter low-prime [103] rusty is its anagram yurts; in addition to the four-letter low triangle [15] cafe is its anagram face; in addition to the five-letter low triangle [21] abide is the word ached; in addiion to the four-letter low square [16] cage are the two words (anagrams of each other) deaf and fade.
Charlie's discovery of the unique seven-letter low triangle and square word [36] bighead requires another word, either a higher low triangle [45] or square [49] word, to be acceptable. As the word needed is in the category of low, and as 45 is less than 49, it would seem that bighead should remain as the square word, and thus I might offer the triangle, obscure word: [45] hambled (mutilated a dog by cutting of the balls of its feet; [obsolete: hamstrung]). If bighead were the triangle word, the square word could be, for instance, [49] beaking (striking with the beak).

Posted by Dej Mar on 2009-03-02 21:50:24