# 4x4 word grid optimization

Given that each letter in the English alphabet has a position: $$a = 1, b = 2, ..., z = 26$$ Can you place 16 different letters such that:

• Each row, column and diagonal forms a 4-letter valid English word. You could use dictionary.com.
• The sum of all letter positions is maximized. That is, using able counts as $$a+b+l+e = 1+2+12+5 = 20$$.

### "And what if such a grid doesn't exist?" — @Bass

For every letter that is used twice or more, all words containing the letter won't count in the total. That is, a beer won't count any point alongside with all other letters in words in the grid that have an e.

• How certain are you that it's possible to create a(n unavoidably double) word square from 16 distinct letters at all, not to even mention the diagonals?
– Bass
Feb 19, 2022 at 12:48
• @Bass, actually, I am not certain at all. I have improved the puzzle thanks to your relevant remark :)
– JKHA
Feb 19, 2022 at 12:57
• Can the diagonals be read in either direction? Feb 20, 2022 at 21:05
• @hexomino, not precised in the puzzle so yes!
– JKHA
Feb 20, 2022 at 22:27

The best I've found so far has a one letter repeat

 T Y M P
H A I L
U N C O
S K E T


With the caveat that

"tymp" does not appear at dictionary.com but does appear on Merriam-Webster. I hope this is acceptable.

I'm not sure how to score this (maybe OP can advise).

• I believe your score is 27, the "double letter negates all points from words using said letter" rule really reduces said score Mar 28, 2022 at 8:24