Question is from here:

Think of two familiar, unhyphenated, eight-letter words that contain the letters A, B, C, D, E and F, plus two others, in any order. What words are these?

Your task is to write a program to find the two words.

My Solution:
Firstly, we need a text file that contains all english words, I managed to find one here. Then all these words are read and stored in a HashSet. Next, I generate all permeation of a given string and check if dictionary contains any of them. When two words are found the program is terminated.

import java.io.*;
import java.util.*;

public class NPR_Sunday_Puzzle {
	//given string
	static String set = "abcdef";
	//for adding two extra letters
	static String [] al = {"a", "b", "c", "d", "e", "f", "g", "h", "i", "j",
			"k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v",
			"w", "x", "y", "z"};
	static Set<String> ans = new HashSet<String>();
	static HashSet<String> dic = new HashSet<String>();

	public static void main(String[] args) {
		long begin = System.currentTimeMillis();
		BufferedReader br = null;
		try {
			String s;
               //locate this file on your PC
			br = new BufferedReader(new FileReader("/enable1.txt"));
			while ((s = br.readLine()) != null) {
				//add English words to HashSet
				dic.add(s);
			}
		} catch (IOException e) {
			e.printStackTrace();
		}
		generate();
		System.out.println("ANS: " + ans);
		long end = System.currentTimeMillis();
		System.out.println("Total execution time: " + (end-begin)/1000 + "s");
	}

	private static void generate(){
		String s = "";

		outter:
		for (int i = 0; i < al.length; i++) {
			for (int j = i + 1; j < al.length; j++) {
				//adding extra two letters
				s += al[i] + al[j];
				permute("", set + s);
				if(ans.size() == 2)
					break outter;
				s = "";
			}
		}

	}
	//generating all permutation of a given string
	public static void permute(String beginningString, String endingString) {
	    if (endingString.length() <= 1){
	    	//check if dic contains the word
	    	if(dic.contains(beginningString + endingString)){
	    		ans.add(beginningString + endingString);
	    		return;
	    	}
	    }
	    else
	      for (int i = 0; i < endingString.length(); i++) {
	        try {
	          String newString = endingString.substring(0, i) + endingString.substring(i + 1);
	          permute(beginningString + endingString.charAt(i), newString);
	        } catch (StringIndexOutOfBoundsException exception) {
	        	exception.printStackTrace();
	        }
	      }
	  }
}

Output:

ANS: [feedback, boldface]
Total execution time: 5s