Duplicity

"He seems pretty impressed, but... he's faking... right?"

- Light Yagami

Duplicity (二枚舌, Nimaijita) is the twenty-first chapter of the Death Note manga series.

Plot
Light expresses amusement by L's sudden announcement that he believes that he is Kira. L tells him that his suspicion is only at one percent as of now, but hopes that Light isn't Kira and thus could be of help in the investigation. For Light, that one percent is still enough to be a threat and for L to deny him a part in the inquiry—which he wants to join in order to better find out their progress and eventually kill L.

Meanwhile, Soichiro Yagami meets with NPA Deputy Director Koreyoshi Kitamura who is becoming frustrated with the increasing secrecy surrounding the Kira Task Force. He is especially annoyed at the fact that someone approached his own daughter claiming to be L. Soichiro assumes that that was Mogi who had been assigned to investigate the Kitamuras over the leaking of police information to Kira.

Currently, the detectives hunting for Kira no longer operate from police HQ: Only one officer at a time stays there is order to take communications. Since he does not know what is going on, Kitamura can assume that the approach to his daughter may not have been a prank. He asks if she is a suspect. Soichiro assures him that this is not the case, because the real suspect is in fact his own son!

Changing the subject, Kitamura remarks that the failure to capture Kira is leading to claims that L and the police are incompetent. Clearly under strain, Soichiro loudly complains about all the resignations from the Kira Task Force, the result being that only a handful of detectives are investigating a case in which any of them could die at any moment! When he's calmed down, Kitamura asks what he thinks of L and if he is trustworthy. Soichiro does admit that L is the most intelligent member of the group and can be trusted since he is currently risking his life in order to solve the case.

Meanwhile, Light and L are at a coffee shop having their chat. Light tells L that he wants to be completely free of suspicion before raising any other issues. L asks if he can test his deductive skills and he agrees. Light is sure that L is hoping to trick him into revealing things that only Kira would know, but is also confident that he knows which facts have been made public and which have not.

L is currently using the alias "Hideki Ryuga", which is also the name of a major celebrity. He begins by asking Light what he makes of his claim to be L. Light suggests that L wants his help but is being cautious: It's public knowledge that Kira needs to know the face of his victim but it could be that he also needs other details, the person's real name for instance. Otherwise why use an obviously false name like "Hideki Ryuga"?

On the other hand, he suggests that "Hideki Ryuga" is not L. L is known for working behind-the-scenes, using the police while remaining safe. He is unlikely to confront Kira himself head-on and would probably send a stand-in, like he did with Lind L. Tailor. If Kira kills the one posing as "Hideki Ryuga" then the real L will know that Light is Kira.

L admits that such a reasoning is coherent with L's habit of sticking to the shadows, but then Light states that he believes him to be L: The public imagine L to be a middle-aged detective so a young man like "Hideki Ryuga" would be a pretty poor choice for a stand-in.

L then shows Light a list of twelve FBI agents who were murdered by Kira, with the order in which they received a certain file, and the order in which they died. Sensing that L wants to see a reaction, Light asks for details of what the file was. L tells him that it was the names and photos of all the agents in Japan and Light suggests that that indicates that Kira, who got a copy of it, really does need those details in order to commit murder.

Some of Kira's victims wrote strange messages on walls before dying;  L shows these messages to Light in the form of photographs. Examining them, Light suggests that this shows that Kira can manipulate his victims into committing certain acts before killing them.

Light has noticed that the photos are numbered but purposely out of order: They are not in the order in which the men wrote the messages and then died. He tells L that, by taking the first word or letter of each line in the messages, this produces another hidden message asking "L do you know Shinigami love apples". L's eyes widen at this revelation (if the messages were in the correct order), but then Light re-arranges them in the order they were numbered which results in "L do you know love apples Shinigami". Light suggests that Kira may have slipped somewhere. Secretly, he feels victorious.

L suddenly produces a fourth photo with another message which concludes that the full hidden message was "L do you know love apples Shinigami have red hands".

Light realizes that L is trying to provoke him, to get him to angrily deny that the fourth message ever existed. Staying calm, he just acknowledges that he did not consider a fourth message and Shinigami don't exist anyway. Ryuk, who can only be seen by Light, makes no comment.

L realizes that Light has not fallen for any of his attempts to catch him out. He now asks light what he would do if he was L and meeting someone suspected of being Kira. Light answers that he would do as L is doing and ask questions to which only the real Kira would know the answers.

L then reveals that he tested the members of the Kira Task Force in a similar way and that they took a while to come up with answers which were rather silly or simplistic. Light on the other hand has come up with very brilliant responses almost instantly and handled them the same way that Kira would have. Light jokes that this has probably made him all the more suspicious, and L seriously confirms that this is the case: His suspicion that Light is Kira has increased to three percent!

Nonetheless, L still wants Light to join the Kira investigation: If he is innocent then he will be a major asset; if he is guilty then he's bound to slip up sooner or later and be found out. He also reveals that there is more than one person claiming to be "L".

Light is taken aback by this implication that there is more than one "L" and also feels narrowed into a corner. However, he then flatly denies being Kira or even wanting to be killed by him—implying that he would rather investigate on an amateur basis using what facts are made public, rather than join the actual investigation and thus become a target for Kira. He even suggests that his current interlocutor may also be Kira. Basically, until someone in the actual Kira Task Force can confirm that he is L, then Light wants nothing to do with him.

This outburst, which includes signs of stubbornness and the desire to win, only increases L's suspicions to seven percent. He then invites Light to actually meet the other detectives involved in the investigation. Light is even more taken aback by this bold offer, but before anything else can be said, their respective cell phones suddenly ring.

The callers on the cell phones give Light and L the same message: Light's father Soichiro has collapsed with a heart attack! Could it be Kira?

Conception
The title "Duplicity," refers to both sides of the conflict are trying to discover what the other side is really thinking.