MathDB

What is the fewest number of multiplications required to reach

x^{2000}

from

x

, using only previously generated powers of

x

? For example

x\rightarrow x^{2}\rightarrow x^{4}\rightarrow x^{8}\rightarrow x^{16}\rightarrow x^{32}\rightarrow x^{64}\rightarrow x^{128}\rightarrow x^{256}\rightarrow x^{512}\rightarrow x^{1024}\rightarrow x^{1536}\rightarrow x^{1792}\rightarrow x^{1920}\rightarrow x^{1984}\rightarrow x^{2000}

uses

15

multiplications.

Problem Statement