Palindrome.java

public class Palindrome {

	// This method checks whether its input reads the same forwards
	// as backwards. For example, isPalindrome("noon") should return
	// true, but isPalindrome("night") should return false.
	
	// Note that this implementation contains a deliberate bug.

	public static boolean isPalindrome(String s) {
		if (s.length() == 0) {
			return true;

		} else {
			char first = s.charAt(0);
			char last = s.charAt(s.length() - 1);

			// Here's the bug... Imagine s is a 1-character string,
			// then the assignment evaluates to:
			// s.substring(1, 1-1) =>
			// s.substring(1, 0) =>
			// StringIndexOutOfBoundsException
			String mid = s.substring(1, s.length() - 1);

			return first == last && isPalindrome(mid);
		}
	}
}

palindrome.rb

class Palindrome
  
  # This method checks whether its input reads the same forwards
  # as backwards. For example, isPalindrome("noon") should return
  # true, but isPalindrome("night") should return false.
  #
  # Note that this implementation contains a deliberate bug.
  
  def is?(s)
    return true if s.size == 0
  
    first, last = s[0], s[s.size-1]
    
    # Here's the bug... Imagine s is a 1-character string,
    # then the assignment evaluates to:
    # s[1, -1] =>
    # nil =>
    # ... causes the s.size == 0 check to fail with NoMethodError
    mid = s[1,s.size-2]
  
    first == last && is?(mid)
  end
end

palindrome_spec.rb

require "palindrome"
require "rspec"

describe Palindrome do
  
# The following 3 tests seem to be sufficient 
# for 100% mutation coverage with mutant
# (I'm using mutant-0.5.22 and the following command
# mutant --include lib --require palindrome --use rspec Palindrome)
  
  it "detects a palindrome" do
    expect(subject.is?("noon")).to be_truthy
  end

  it "detects a non-palindrome" do
    expect(subject.is?("midnight")).to be_falsey
  end

  it "detects not quite palindrome" do
    expect(subject.is?("neon")).to be_falsey
  end

# This additional test is needed to kill the mutant
# mid = s[1,2]

  it "detects a longer palindrome" do
    expect(subject.is?("hannah")).to be_truthy
  end

# However the following test is needed to reveal the bug
# Is there a mutant that would cause us to discover the need 
# for this test?

  # it "detects odd length palindrome" do
  #   expect(subject.is?("radar")).to be_true
  # end
  
# Additonally, to achieve 100% path coverage, I think that
# we'd also need the following test case. Is there a mutant
# that would cause us to discover the need for this case?
  
  # it "detects empty string palindrome" do
  #   expect(subject.is?("")).to be_true
  # end
end

PalindromeTests.java

import static org.junit.Assert.*;
import static palindrome.Palindrome.isPalindrome;

import org.junit.Test;

public class PalindromeTests {

// The following 3 tests seem to be sufficient 
// for 100% mutation coverage with PIT
// (I'm using PITclipse v0.33.2.201404202230)
	
	@Test
	public void detectsPalindrome() {
		assertTrue(isPalindrome("noon"));
	}

	@Test
	public void detectsNonPalindrome() {
		assertFalse(isPalindrome("midnight"));
	}

	@Test
	public void detectsNotQuitePalindrome() {
		assertFalse(isPalindrome("neon"));
	}
	
// However the following test is needed to reveal the bug
// Is there a mutant that would cause us to discover the need 
// for this test?

//	@Test
//	public void detectsOddPalindrome() {
//		assertTrue(isPalindrome("eve"));
//	}
	
	
// Additonally, to achieve 100% path coverage, I think that
// we'd also need the following test case. Is there a mutant
// that would cause us to discover the need for this case?
	
//	@Test
//	public void detectsEmptyStringPalindrome() {
//		assertTrue(isPalindrome(""));
//	}
}

This requires a higher order mutant. I ran Mutator 1.7 (http://ortask.com/mutator/) to create a second order mutant and was able to easily find a live mutant that surfaces the need for the missing test. Here's the mutant:

public class Palindrome {
    public static boolean isPalindrome(String s) {
        if (s.length() == 0) {
            return true;

        } else {
            char first = s.charAt(1);               // <--- originally 0. 
            char last = s.charAt(s.length() - 2);   // <--- originally 1. 

            String mid = s.substring(1, s.length() - 1);

            return first == last && isPalindrome(mid);
        }
    }
}