Rise and shine, Mister Bond.
James awoke to find himself yet again imprisoned by an evil genius. At least, that's what he presumed. He was alone in a room with a strange device: it consisted of a person-sized glass chamber, with a single tube feeding out of it, splitting into 23 tubes which headed God knows where.
I do hope you're comfortable, since you will be here for quite a while. We're going to play a little game.
The voice was coming from an intercom. "If it's information you want, you might as well kill me. I'll die before I tell you anything!"
Nothing so routine, Mister Bond. What I want is to test your mettle. The device in front of you is a cloning machine: it will completely vaporize your body, but will create 23 identical copies in your place, each to be housed in separate prison cells.
After this I will, at random times, bring a random clone out of his cell into the Light Bulb Room. This room has two lightbulbs, one red and one blue, which are each either on or off. The clone may then toggle none, either or both of the bulbs, before I return him to his cell. I will take care to ensure the clones can't communicate with each other, or change the Light Bulb Room in any other way then toggling these bulbs.
"And what exactly am I supposed to accomplish through all this?"
A clone may at any time make the declaration that every clone has visited the Light Bulb Room room. If he is right, you win and may all go free. If he is wrong, you will all be executed.
I'll give you some time to think of a plan before this begins. Since my machine copies your brain state exactly, all of the clones will follow the exact same plan.
Time to see if you really are the stuff of legends, Mister Bond.
"Wait! What did you say the initial states of the light bulbs were?"
A faint crackling, then silence.
How can James Bond succeed, with certainty?
Compare and contrast this with the classic "100 prisoners and one lightbulb" puzzle. In that one, the prisoners could use an asymmetric strategy where one prisoner was singled to count the others. This asymmetry is now ruled out since all prisoners are clones. The winning strategy will require the extra power of having two light bulbs.