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A's and B's

Find all 5-letter words consisting solely of the letters A and B, such
that there are no words with three repeated characters in a row (no
AAAxx, xAAAx, or xxAAA words.) There are 16 such words.
Make a 5x5 grid of A's and B's, such that
each row (read left to right), column (read top to bottom), and the
two diagonals (read top to bottom) is a different one of these words.
Follow-up: how many such squares are there? Is it possible
to make a square in which all the words beginning with "A" can be
found?
Source: Original. Based upon
Macalester College Problem of the Week #965, which asked the
4-letter version of this problem, of which there is a single solution.

Solutions were received from Denis Borris and Al Zimmermann. Al's
solution follows:
There are 20 solutions. Here are 10 of them. The other 10 can be
obtained by swapping the A's for B's and vice-versa. Only the first
solution below contains all 8 allowable words beginning with A.
A A B A A A A B B A A A B B A A B A B A A B A B A
B B A B A B A A B B B B A B B B A A B B B A B A A
B B A A B A B B A A A A B A A A B B A A A B B A B
A A B B A B A B A B B A B A B B A B A A B A A B A
B A B A B B B A B A B B A B A B B A B B B B A B A
A B A B B A B A B B A B A B B A B A B B A B B A B
A B A A B B A B A B B A B A B B A B A B A B B A A
B A B B A A A B A A A A B B A A A B B A B A A B B
A A B A B B B A B B B B A A B B B A A B A B A B A
A B A B A A B B A A A B A A B A B B A A A A B A B

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