Using the relationship [A=1, B=2,..... Z=26] provide a word for each tier of the triangle such that:
1. The letter sum per tier is the largest square possible.
2. The letter sum per tier is the smallest square possible.

While being squares neither SEA = 25 nor OAT = 36 are appropriate for tier three in either of the tasks #1 or #2 above.

Are you able to extend either triangle beyond 6 tiers?

(In reply to computer solutions by Charlie)

Taxonomy of Wordplay is a site with various word trivia, including a list of shortest and longest words with smallest and largest "letter sum" values (though not for the specific nature of square values). From the 'smallest value' list is a word that has a smaller square value than in Charlie's list and from the 'largest value' list is a word that has a larger square value than in Charlie's list. Both probably due to these words being identified as uncommon.

Word   Word in        Word        Word in             Word
Length Charlie's List Value Squ ToW                 Value  Squ
14       cleanabilities 121    11   hamamelidaceae  81     9 (-2)

5         nutty            100    10   wuzzy                121   11 (+1)**
**(I, myself, had also previously listed the uncommon 5-letter words with word value 100, purty and zitty, for the 5th tier. For the same tier, wuzzy has a greater square value.) 

Posted by Dej Mar on 2012-09-08 13:54:53