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Ok, we have 2 hat placements: same color next to each other, or same color across.

If same color across (assume black hat asked first):
The only way to be the first person and know your hat is to see 2 of the same color and the red hat.

• First person (sees white, white, black): IDK
• Second (bbw): IDK
• Third (wwb): Knows that the black hat across from him didn't see a red hat on his head, Black
• Fourth (bbw): Same as third, but White
• First (wwb): Knows that he has black or red. Second's answer doesn't help (could see wbr), neither does third (could see wwr). Fourth's though indicates that his color is the same as the guy's across, so Black
• Second (bbw): can use same logic as first and go White

And the colors sitting next to each other (go order BBWW):

• First (wwb): IDK
• Second (wwb): Sees the same WW that first did, knows he's not R, so Black
• Third (bbw): Sees the same WB that first did, IDK
• Fourth (bbw): Sees the same BB that third did, knows he's not R, so White
• First (wwb): knows second could have seen red or black and gotten his hat, knows it doesn't matter for third, but knows fourth had to see some dupe. Since first already sees the ww dupe, he knows his hat is Black
• Third (bbw): uses same logic as first to get his hat as White

For the sake of completeness, lets' go with a variant of scenario 2 (order BWWB):

• First (wwb): IDK
• Second (bbw): IDK
• Third (bbw): Sees the same BB that second did, know's he's not R, so White
• Fourth (wwb): Sees the same WW that first did, know's he's not R, so Black
• First (wwb): Knows that both second and third saw BWX, and both of them see BWX, and the second one knows something the first doesn't, which is that both of them see a pair. He would think he is black, but then if he were R, then third would know why second was stuck, and fourth would know his color straight up. IDK
• Second (bbw): If he were R, then third's declaration would be the same, as would fourth's (based on first). IDK
• Stuck

Ok, we have 2 hat placements: same color next to each other, or same color across.

If same color across (assume black hat asked first):
The only way to be the first person and know your hat is to see 2 of the same color and the red hat.

• First person (sees white, white, black): IDK
• Second (bbw): IDK
• Third (wwb): Knows that the black hat across from him didn't see a red hat on his head, Black
• Fourth (bbw): Same as third, but White
• First (wwb): Knows that he has black or red. Second's answer doesn't help (could see wbr), neither does third (could see wwr) nor fourth (could see wbr and determine that second also has wbr). IDK
• Second (bbw): if red, then first's idk, third's I know, and fourth's I know are all reasonable. IDK
• Stuck.

And the colors sitting next to each other (go order BBWW):

• First (wwb): IDK
• Second (wwb): Sees the same WW that first did, knows he's not R, so Black
• Third (bbw): Sees the same WB that first did, IDK
• Fourth (bbw): Sees the same BB that third did, knows he's not R, so White
• First (wwb): knows second could have seen red or black and gotten his hat, knows it doesn't matter for third, but knows fourth had to see some dupe. Since first already sees the ww dupe, he knows his hat is Black
• Third (bbw): uses same logic as first to get his hat as White

For the sake of completeness, lets' go with a variant of scenario 2 (order BWWB):

• First (wwb): IDK
• Second (bbw): IDK
• Third (bbw): Sees the same BB that second did, know's he's not R, so White
• Fourth (wwb): Sees the same WW that first did, know's he's not R, so Black
• First (wwb): Knows that both second and third saw BWX, and both of them see BWX, and the second one knows something the first doesn't, which is that both of them see a pair. He would think he is black, but then if he were R, then third would know why second was stuck, and fourth would know his color straight up. IDK
• Second (bbw): If he were R, then third's declaration would be the same, as would fourth's (based on first). IDK
• Stuck

Ok, we have 2 hat placements: same color next to each other, or same color across.

If same color across (assume black hat asked first):
The only way to be the first person and know your hat is to see 2 of the same color and the red hat.

• First person (sees white, white, black): IDK
• Second (bbw): IDK
• Third (wwb): Knows that the black hat across from him didn't see a red hat on his head, Black
• Fourth (bbw): Same as third, but White
• First (wwb): Knows that he has black or red. Second's answer doesn't help (could see wbr), neither does third (could see wwr). Fourth's though indicates that his color is the same as the guy's across, so Black
• Second (bbw): can use same logic as first and go White

And the colors sitting next to each other (go order BBWW):

• First (wwb): IDK
• Second (wwb): Sees the same WW that first did, knows he's not R, so Black
• Third (bbw): Sees the same WB that first did, IDK
• Fourth (bbw): Sees the same BB that third did, knows he's not R, so White
• First (wwb): knows second could have seen red or black and gotten his hat, knows it doesn't matter for third, but knows fourth had to see some dupe. Since first already sees the ww dupe, he knows his hat is Black
• Third (bbw): uses same logic as first to get his hat as White

For the sake of completeness, lets' go with a variant of scenario 2 (order BWWB):

• First (wwb): IDK
• Second (bbw): IDK
• Third (bbw): Sees the same BB that second did, know's he's not R, so White
• Fourth (wwb): Sees the same WW that first did, know's he's not R, so Black
• First (wwb): Knows that both second and third saw BWX, and both of them see BWX, and the second one knows something the first doesn't, which is that both of them see a pair. They are white, so he is Black
• Second (bbw): Same as first, White

Ok, we have 2 hat placements: same color next to each other, or same color across.

If same color across (assume black hat asked first):
The only way to be the first person and know your hat is to see 2 of the same color and the red hat.

• First person (sees white, white, black): IDK
• Second (bbw): IDK
• Third (wwb): Knows that the black hat across from him didn't see a red hat on his head, Black
• Fourth (bbw): Same as third, but White
• First (wwb): Knows that he has black or red. Second's answer doesn't help (could see wbr), neither does third (could see wwr). Fourth's though indicates that his color is the same as the guy's across, so Black
• Second (bbw): can use same logic as first and go White

And the colors sitting next to each other (go order BBWW):

• First (wwb): IDK
• Second (wwb): Sees the same WW that first did, knows he's not R, so Black
• Third (bbw): Sees the same WB that first did, IDK
• Fourth (bbw): Sees the same BB that third did, knows he's not R, so White
• First (wwb): knows second could have seen red or black and gotten his hat, knows it doesn't matter for third, but knows fourth had to see some dupe. Since first already sees the ww dupe, he knows his hat is Black
• Third (bbw): uses same logic as first to get his hat as White

For the sake of completeness, lets' go with a variant of scenario 2 (order BWWB):

• First (wwb): IDK
• Second (bbw): IDK
• Third (bbw): Sees the same BB that second did, know's he's not R, so White
• Fourth (wwb): Sees the same WW that first did, know's he's not R, so Black
• First (wwb): Knows that both second and third saw BWX, and both of them see BWX, and the second one knows something the first doesn't, which is that both of them see a pair. He would think he is black, but then if he were R, then third would know why second was stuck, and fourth would know his color straight up. IDK
• Second (bbw): If he were R, then third's declaration would be the same, as would fourth's (based on first). IDK
• Stuck

If same color across (assume black hat asked first):
The only way to be the first person and know your hat is to see 2 of the same color and the red hat.
First person (sees white, white, black): IDK
Second (bbw): IDK
Third (wwb): Knows that the black hat across from him didn't see a red hat on his head, Black Fourth (bbw): Same as third, but White
First (wwb): Knows that he has black or red. Second's answer doesn't help (could see wbr), neither does third (could see wwr). Fourth's though indicates that his color is the same as the guy's across, so Black
Second (bbw): can use same logic as first and go White

And the colors sitting next to each other (go order BBWW):
First (wwb): IDK
Second (wwb): Sees the same WW that first did, knows he's not R, so Black
Third (bbw): Sees the same WB that first did, IDK
Fourth (bbw): Sees the same BB that third did, knows he's not R, so White
First (wwb): knows second could have seen red or black and gotten his hat, knows it doesn't matter for third, but knows fourth had to see some dupe. Since first already sees the ww dupe, he knows his hat is Black
Third (bbw): uses same logic as first to get his hat as White

For the sake of completeness, lets' go with a variant of scenario 2 (order BWWB):
First (wwb): IDK
Second (bbw): IDK
Third (bbw): Sees the same BB that second did, know's he's not R, so White
Fourth (wwb): Sees the same WW that first did, know's he's not R, so Black
First (wwb): Knows that both second and third saw BWX, and both of them see BWX, and the second one knows something the first doesn't, which is that both of them see a pair. They are white, so he is Black
Second (bbw): Same as first, White

If same color across (assume black hat asked first):
The only way to be the first person and know your hat is to see 2 of the same color and the red hat.

• First person (sees white, white, black): IDK
• Second (bbw): IDK
• Third (wwb): Knows that the black hat across from him didn't see a red hat on his head, Black
• Fourth (bbw): Same as third, but White
• First (wwb): Knows that he has black or red. Second's answer doesn't help (could see wbr), neither does third (could see wwr). Fourth's though indicates that his color is the same as the guy's across, so Black
• Second (bbw): can use same logic as first and go White

And the colors sitting next to each other (go order BBWW):

• First (wwb): IDK
• Second (wwb): Sees the same WW that first did, knows he's not R, so Black
• Third (bbw): Sees the same WB that first did, IDK
• Fourth (bbw): Sees the same BB that third did, knows he's not R, so White
• First (wwb): knows second could have seen red or black and gotten his hat, knows it doesn't matter for third, but knows fourth had to see some dupe. Since first already sees the ww dupe, he knows his hat is Black
• Third (bbw): uses same logic as first to get his hat as White

For the sake of completeness, lets' go with a variant of scenario 2 (order BWWB):

• First (wwb): IDK
• Second (bbw): IDK
• Third (bbw): Sees the same BB that second did, know's he's not R, so White
• Fourth (wwb): Sees the same WW that first did, know's he's not R, so Black
• First (wwb): Knows that both second and third saw BWX, and both of them see BWX, and the second one knows something the first doesn't, which is that both of them see a pair. They are white, so he is Black
• Second (bbw): Same as first, White