HELP!!!! MATH PROBLEM

[Jd-]

Guesses = not answers, matey.

[GinRei]

Let's give this a whirl, Kogorou Style!

For all intents and purposes, the first man will be known as "Akai" due to giving a red piece of paper and the second man will be known as "Midori" for giving a green piece of paper.

Spoiler:

First off, the conditions of the boxes.

Akai knows the results of all three boxes.  The specific contents do not matter, only whether the box is "correct" or "incorrect."  Therefore, by knowing two of the boxes, he actually knows all three, as he'd either have knowledge of two incorrect (forcing the third to be correct) or an incorrect and a correct (forcing the third to be incorrect).

Midori, despite supposedly be honest, lies to you right off the bat.  He claims to know the content of all three boxes, yet he only knows one box.  This proves that whatever he says cannot be trusted, and as such the suggestion that the green box holds the correct answer is a lie as well.

Now, with only two boxes remaining, all further proof lies on Akai.  Knowing that he is slightly devious (or "dependably dubious"), and also that he wants to win at all costs... that is the key to this mystery!  Remember, both Akai and Midori's favorite colors are red.  Furthermore, both would rather you win than their opponent.  From here, Akai has two ways of winning.

The first method of winning is the obvious obtaining of the correct box.  This does not assist in the investigation at all, though it is important to note.

The second method is to not only prevent Midori from getting the correct box, but to dominate him psychologically.  The way to accomplish this?  Obtain the red box for himself!

In other words... the correct box is BLUE!  Either you choose the blue box, securing your own victory and allowing Akai to obtain the red box, or you choose the red box and Akai secures the blue box.

If you happened to follow Midori's advice and choose green, then Akai already knows that Midori will have a mere 50% chance of obtaining the correct box.  When faced with those odds, one generally goes for their favorite color, so Midori would go with the red box, also securing Akai's victory.

[Jd-]

Let's give this a whirl, Kogorou Style!

For all intents and purposes, the first man will be known as "Akai" due to giving a red piece of paper and the second man will be known as "Midori" for giving a green piece of paper.

Spoiler:

First off, the conditions of the boxes.

Akai knows the results of all three boxes.  The specific contents do not matter, only whether the box is "correct" or "incorrect."  Therefore, by knowing two of the boxes, he actually knows all three, as he'd either have knowledge of two incorrect (forcing the third to be correct) or an incorrect and a correct (forcing the third to be incorrect).

Midori, despite supposedly be honest, lies to you right off the bat.  He claims to know the content of all three boxes, yet he only knows one box.  This proves that whatever he says cannot be trusted, and as such the suggestion that the green box holds the correct answer is a lie as well.

Now, with only two boxes remaining, all further proof lies on Akai.  Knowing that he is slightly devious (or "dependably dubious"), and also that he wants to win at all costs... that is the key to this mystery!  Remember, both Akai and Midori's favorite colors are red.  Furthermore, both would rather you win than their opponent.  From here, Akai has two ways of winning.

The first method of winning is the obvious obtaining of the correct box.  This does not assist in the investigation at all, though it is important to note.

The second method is to not only prevent Midori from getting the correct box, but to dominate him psychologically.  The way to accomplish this?  Obtain the red box for himself!

In other words... the correct box is BLUE!  Either you choose the blue box, securing your own victory and allowing Akai to obtain the red box, or you choose the red box and Akai secures the blue box.

If you happened to follow Midori's advice and choose green, then Akai already knows that Midori will have a mere 50% chance of obtaining the correct box.  When faced with those odds, one generally goes for their favorite color, so Midori would go with the red box, also securing Akai's victory.

This is...

Spoiler:

INDEED THE CORRECT ANSWER!

*starts a slow clap*

Bravo to GinRei-chankunsamashi.

The deceit in the question is, indeed, the honesty that Man 2 supposedly possesses. What's important is what it says immediately after--that he is envious. From seeing the conditions he's under and the lie that he will tell when asked (that he knows all 3, but really only knows 1), you can conclude his proclivity for telling the truth does not have precedence over his jealousy for his counterpart. Thus, why he will lie in order to seem more reputable.

The real trick here, as GinRei has correctly pointed out, is to understand that Man 1 knows all 3 boxes right off the bat, but because of the way it's phrased, it doesn't immediately come to mind that this is the case. With that, the puzzle is no longer of the deductive nature but of the preemptive sort--your goal is no longer to figure out which order to go in, but instead just to not let Man 1 go ahead of you. Given that you can deduce he actually does know all 3, it's as simple as concluding the blue box is the correct one and going first. As is outlined in the problem, Man 1 wants to win so long as his enemy does not--that is the most important piece of information. Because of this, if he is allowed to go ahead of you, he will choose the blue and ultimately correct box.

We know that, because he is dubious in nature, Man 1 will lie to you if he sees the opportunity, and he does. That is why he recommends the wrong box that also happens to be his favored color--it's merely misdirection to make you choose that box.

But, there is one last piece of information to take into account... While Man 1 may know all 3 boxes, what does Man 2 know? He really only know what's inside one box, so what if you let him go first in the event you weren't sure? Well, as GinRei hinted at, he is likely to take the red one--so long as he isn't aware that the red one isn't the correct one. If the one he knows is the blue one, then he may take the box for himself initially and ensure that you lose. As such, the only way to ensure victory for yourself is to choose to go first, take the blue box, and let the rest go as it will.

(The reason I extrapolated on this last bit is because I had someone mention it once, so thought it'd be of interest here as well )

[Found]

Spoiler:

Does GinRei get the special title you mentioned?

[GinRei]

JD told ginrie the answer so nobody gers the title 

No he didn't.  I have the best title on here anyway, so I don't need some crazy off-topic title.