MathDB

Suppose there is an infinite sequence of lights numbered

1, 2, 3,...,

and you know the following two rules about how the lights work:

\bullet

If the light numbered

k

is on, the lights numbered

2k

and

2k + 1

are also guaranteed to be on.

\bullet

If the light numbered

k

is off, then the lights numbered

4k + 1

and

4k + 3

are also guaranteed to be off. Suppose you notice that light number

2023

is on. Identify all the lights that are guaranteed to be on?

Problem Statement