When Will The World End “Temple of Brahma” legend from the Indian city of Benares Priests must move 64 gold disks from one end of the temple to the other Disks may only be moved one at a time, and a larger disk may never be placed on a smaller disk There is only one intermediate spot where a disk may be placed. When the last disk is placed on the stack the world will vanish in a clap of thunder.

Origin of “Tower of Hanoi” Edouard Louis, French mathematician, 1883 Tower of Hanoi at MazeWorks

Recursive Pattern Let M = the number of moves to move (n-1) disks to position 2. [M moves] Move disk 1 to position 3. [1 move] Move (n-1) disks to position 3. [M moves] Total number of moves 2M + 1

Number of disks 1 2 3 4 5 Number of moves 1 3 7 15 31

Explicit Pattern Find a pattern. Hint: add 1 to each number of moves Number of moves at n: a(n)=2n-1 Can be proven with induction Hint

When will the World End If it takes 1 second for the monks to move each disk, then the world will end in 264-1 seconds. 1.84 x 1019 seconds. 5.12 x 1015 hours. 5.85 x 1011 years.

When will the World End That’s 585 billion years!!! End Show

Number of disks 1 2 3 4 5 Number of moves 1 + 1 = 2 3 + 1 = 4 7 + 1 = 8 15 + 1 = 16 31 + 1 = 32 Return