RB_CH01_Q013. 100 light bulbs and 100 stockbrokers

There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 stockbrokers lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. Each stockbroker is also numbered consecutively from 1 to 100. Broker number 1 enters the room, switches on every bulb, and exits. Broker number 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, ...). Broker number 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, ...). This continues until all 100 brokers have passed through the room. What is the final state of bulb number 64? Is it illuminated or dark?