Palindrome Checker Algorithm
Since the char array sizes are fixed, you should make sure the inputs are of an appropriate size before continuing.  This should best be done with the function doing the reading.

Very important: gets() is unsafe as it has no knowledge of buffer size thus is vulnerable to buffer overflow.  Instead, use fgets(), which is safer as it takes a buffer size as an argument.
Consider hard-coding the 50 to make its intent clear.

#define MAX_LENGTH 50

Since you're already in main(), you can use return 1 instead of exit(1).
Unformatted strings like this:


printf("Please enter a string: ");



can instead be output using puts():

puts("Please enter a string: ");


Be aware that puts() automatically appends a newline at the end.  If you don't want this newline, then you can use fputs() instead:

fputs("Please enter a string: ", stdout);