1. ECE 103 Engineering Programming
Chapter 1
Towers of Hanoi
Herbert G. Mayer, PSU
Status 7/16/2018

2. Syllabus Story Behind The Exact Rules Small Tower with 5 Disks
Hanoi in C
Program Output
Bibliography

3. Story Behind Towers of Hanoi
Puzzle was invented by French mathematician Édouard Lucas in 1883
The story: An Indian temple contains a large room with three time-worn posts in it, surrounded by 64 golden disks
Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks in accordance with the immutable rules of Brahma since that time
The puzzle is also known as the Tower of Brahma Puzzle.
According to legend, when the last move of the puzzle is completed, the world will end 

4. Story Behind Towers of Hanoi
If the story were true, and if the priests were able to move disks one per second
Using the smallest number of moves, then
It would take the priests 264 − 1 seconds or roughly 585 billion years to finish
Which is about 40 times the age of the universe
Don't wait for it to happen, complete your ECE degree first! 

5. The Exact Rules
We have a tower of 64 disks at Start, stacked on top of one another
There are three places: Start, Buffer, and Goal
Initially all 64 discs are stacked on top of one another on the Start pin
All disks have different sizes
A larger disk may never rest on a smaller disk
Goal: The whole tower of 64 disks is to be moved, one disk at a time, from Start, to Goal, using only the 3 places Start, Buffer, and Goal
Try it with just 3 or 4 disks to become familiar

6. Small Tower with 5 Disks

7. Hanoi in C #include <stdio.h> void hanoi( int discs,
char* start, char* buff, char* goal );
// Towers with disks
int main( void )
{ // main
for( int d = 1; d < 5; ++d ) {
printf( "Moving %d discs.\n", d );
hanoi( d, "start", "buff ", "goal " );
printf( "\n" );
} //end for
return 0;
} //end main

8. Hanoi in C void hanoi( int discs,
char* start, char* buff, char* goal )
{ // hanoi
if( discs > 0 ) {
hanoi( discs-1, start, goal, buff );
printf( "Move disc %d from %s to %s\n“,
discs, start, goal );
hanoi( discs-1, buff, start, goal );
} //end if
} //end hanoi

9. Program Output 1 .. 3 Moving 1 discs. Move disc 1 from start to goal
Move disc 1 from start to buff
Move disc 2 from start to goal
Move disc 1 from buff to goal
Moving 3 discs.
Move disc 2 from start to buff
Move disc 1 from goal to buff
Move disc 3 from start to goal
Move disc 1 from buff to start
Move disc 2 from buff to goal

10. Program Output 4 Moving 4 discs. Move disc 1 from start to buff
Move disc 2 from start to goal
Move disc 1 from buff to goal
Move disc 3 from start to buff
Move disc 1 from goal to start
Move disc 2 from goal to buff
Move disc 4 from start to goal
Move disc 2 from buff to start
Move disc 3 from buff to goal

11. Bibliography Wiki: https://en.wikipedia.org/wiki/Tower_of_Hanoi
Mayer, Herbert; Perkins, Don (1984). "Towers of Hanoi Revisited". SIGPLAN Notices. 19 (2): 80–84