(related to Problem: The Deified Puzzle)
The correct answer is $1,992$ different ways. 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 $16 \times 16 = 256$ ways. Consequently, the four corner $F$'s give $4 \times 256 = 1,024$ ways. 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 $8 \times 121 = 968$ ways. 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 $400.$
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