# Heteropalindromes in a Word Square

Say hello to a not-so-simple, 4x4 word square:

This little monstrosity has two rules; to define the first rule, have you ever heard of a heteropalindrome?

Strings of letters that form words when read both forward and backward (e.g., "deliver" and "reviled") are termed heteropalindromes.

Now you have, and with that out of the way; the first rule is that the result for each row and column, must be classified as a heteropalindrome, as described above. For example:

[s, a, g, a]
[p,  ,  ,  ]
[a,  ,  ,  ]
[s,  ,  ,  ]


The second rule is simply that words must be contained in YAWL.

Your task is simple, complete the word square, while meeting the aforementioned constraints. The first answer meeting the aforementioned requirements will get the checkmark.

• Are repeated words okay?
– Deusovi
Sep 16, 2021 at 20:49
• @Deusovi yes, they are. Sep 16, 2021 at 20:50
• are true palindromes allowed? Sep 16, 2021 at 20:54
• @SteveV of course :) since repeated words are okay. Sep 16, 2021 at 21:22

[W, A, R, D]
[A, J, A, R]
[R, A, J, A]
[D, R, A, W]

Yet another one, with all 16 words different: (I admit that this is a computer-assisted answer, in the sense that I wrote a program to extract the list of 4-letter heteropalindromes from YAWL. I constructed the square manually from that list.)

alan
rima
even
sena

For side information: there are only 16 unique such squares containing 16 unique words (not counting rotations and reflections of same grids), which can be verified via this script.

There are 2720 unique squares in total if duplicate words and palindromes are allowed. Notably, under this rule, there are a few very trivial answers due to the property of certain words like

anan
nana
anan
nana

abba
boob
boob
abba

anna
naan
naan
anna

Finally, there is exactly one grid that manages to have one diagonal also being a heteropalindrome and the other diagonal containing vowels and being a palindrome (but unfortunately not a word in YAWL):

eses
slee
eels
sese

[P, E, T, S]
[E, D, I, T]
[T, I, D, E]
[S, T, E, P]