Solution for Section 8.1 Question 5

5. a)  From page 430 of the textbook, m₁ = 1.

b) From page 430 of the textbook,  m_n = 2 · m_n-1 + 1 for all integers n2.

c) Since  m₆ = 63,  m₇ =  2 · m₆ + 1 = 127.  So it will take at least 127 moves to move a tower of 7 disks from one pole to another.

d) To calculate the value of m₁₂, we need to find all the previous terms.
m₈ = 2 · m₇ + 1 = 255.
m₉ = 2 · m₈ + 1 = 511.
m₁₀ = 2 · m₉ + 1 = 1023.
m₁₁ = 2 · m₁₀ + 1 = 3070.
m₁₂ = 2 · m₁₁ + 1 = 6141.  

Back to Section 8.1