Pinks alternately lie and tell the truth, when speaking to visitors and they never forget whether the last statement they made was truth or lie.
(1) I'm in the Pink,
(2) White's in the White, and
(3) Red's a Red
According to the pink party they lie first therefore pink is not a pink, white is a white and red is not a red, so pink is in the red party white is in the white and red is in the pink party.
Its probably wrong but it looks good to me.