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 computer solution by Charlie)

Charlie,
other than the prime words: bad [7], aced [13], putz [83] and quixotry [149]; the triangle words: cab [6], wry [66], onyx [78] and fusty [91]; and the square word-prefix: oxy [64]; those words offered violate the condition that each letter must be distinct within a word. For instance, tut [61], though prime, has two 't's, thus does not fit the category. Oxy, as you noted, doesn't fit the category as it is only a word prefix.

Posted by Dej Mar on 2009-02-28 21:17:43