Problem 5 Output.txt

/* Jay Hankins
 * Avon High School
 * IUPUI Math Contest - Problem #5
 * 
 * Original Contest Problem:
 * You have ten Scrabble
 * tiles with the letters A E F G I L M N O S in that
 * order. Your task is to shuffle them around to obtain a ten-letter English word (there
 * is only one). However, you are only allowed two types of manipulation: you can shift
 * the first letter to the last position, and you can pick the letters in odd positions (in
 * order) followed by the letters in even positions (in order). Thus, starting with the
 * letters in alphabetic order, you can reach E F G I L M N O S A , and A
 * F I M O E G L N S . What is the shortest sequence of moves needed to
 * complete the task?

 * This Java program outputs the number position result of the word "flamingoes," the only 
 * 10-letter English word than can be spelled from the given letters, by performing the 
 * operations like a recursion tree (see diagram). 
 * Note: This program does not output the number of "tries" or "moves" to get to 
 * "flamingoes." I will explain the logic behind deducing the number of moves from the position by hand.
 */
 
Program Output:
WORD					  	   MOVE TYPE AND DESCRIPTION 		 MOVE #
=========================================================================				
AEFGILMNOS //line 1, 										 	 move 0.
EFGILMNOSA //line 2 = 		even 	= first to last letter, 	 move 1.
FGILMNOSAE //line 4 = 		even 	= first to last letter, 	 move 2.
FIMOAGLNSE //line 9 = 		odd 	= odd then even letters, 	 move 3.
FMALSIOGNE //line 19 = 		odd 	= odd then even letters, 	 move 4.
FASONMLIGE //line 39 = 		odd 	= odd then even letters, 	 move 5.
FSNLGAOMIE //line 79 = 		odd 	= odd then even letters, 	 move 6.
SNLGAOMIEF //line 158 =		even 	= first to last letter, 	 move 7.
SLAMENGOIF //line 317 = 	odd		= odd then even letters, 	 move 8.
SAEGILMNOF //line 635 = 	odd 	= odd then ever letters, 	 move 9.
SEIMOAGLNF //line 1271 =	odd 	= odd then even letters, 	 move 10.
EIMOAGLNFS //line 2542 = 	even 	= first to last letters, 	 move 11.
IMOAGLNFSE //line 5084 = 	even 	= first to last letters, 	 move 12.
IOGNSMALFE //line 10169 = 	odd 	= odd then even letters,	 move 13.
IGSAFONMLE //line 20339 =	odd 	= odd then even letters, 	 move 14.
ISFNLGAOME //line 40679 = 	odd 	= odd then even letters, 	 move 15.
SFNLGAOMEI //line 81358 = 	even 	= first to last letters,  	 move 16.
FNLGAOMEIS //line 162716 = 	even	= first to last letters, 	 move 17.
FLAMINGOES //line 325433 = 	odd 	= odd then even letters,  	 move 18.