MathDB

There are 2021 light bulbs in a row, labeled 1 through 2021, each with an on/off switch. They all start in the off position when 1011 people walk by. The first person flips the switch on every bulb; the second person flips the switch on every 3rd bulb (bulbs 3, 6, etc.); the third person flips the switch on every 5th bulb; and so on. In general, the

k

th person flips the switch on every

(2k - 1)

th light bulb, starting with bulb

2k - 1

. After all 1011 people have gone by, how many light bulbs are on?

Problem Statement