The correct answer is 1,992 different
Every F is either a corner F or a side F—standing next to a
corner in its own square of F's.
Now, FIED may be read from a corner F in 16 ways;
therefore DEIF may be read into a corner F also in
16 ways; hence DEIFIED may be read through a corner
F in 16 × 16 = 256
Consequently, the four corner F's give
4 × 256 = 1,024
Then FIED may be read from a side F in 11 ways, and DEIFIED therefore
in 121 ways.
But there are eight side F's; consequently these give together
8 × 121 = 968
Add 968 to 1,024 and we get the answer, 1,992.
In this form the solution will depend on whether
the number of letters in the palindrome be odd or even.
For example, if you apply the word NUN in precisely the same manner,
you will get 64 different readings; but if you use the word NOON, you
will only get 56, because you cannot use the same letter twice in
immediate succession (since you must "always pass from one letter to
another") or diagonal readings, and every reading must involve the use
of the central N.
The reader may like to find for himself the
general formula in this case, which is complex and difficult. I will
merely add that for such a case as MADAM, dealt with in the same way as
DEIFIED, the number of readings is 400.