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    \$\begingroup\$ Suggested test case: xyxxxyx, It's a palindrome and its halves contain non-trivial palindromes but are not actually palindromes themselves. \$\endgroup\$ Commented Jan 19, 2022 at 9:36
  • \$\begingroup\$ Palindromess? Palindromeness? Palindromosity? Palindromity? \$\endgroup\$ Commented Jan 19, 2022 at 14:15
  • \$\begingroup\$ @DJClayworth Palindromicity? \$\endgroup\$ Commented Jan 19, 2022 at 19:05
  • \$\begingroup\$ I don't find it clear what a triple palindrome is from the description and examples so far (it's not clear how to generalize "halves"), much less higher order palindromes. \$\endgroup\$ Commented Jan 20, 2022 at 5:32
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    \$\begingroup\$ @GregMartin Okay, the concept of "half". If the string has equal length, the half is just half of the string (ex. "format", a half would be "for" or "mat" ). If the string has odd length, you include the center character (ex. "hello", a half would be "hel" or "llo"). It doesn't matter which half you choose. If one of the halves is a palindrome, then they are identical. Anyways, a triple palindrome is a palindrome, whose halves are double palindromes. \$\endgroup\$ Commented Jan 20, 2022 at 5:45