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Colors and binarity provide important constraints on the Kuiper belt formation. The cold classical objects at radial distance r=42-47 au from the Sun are predominantly very red (spectral slope s>17%) and often exist as equal-size binaries (~30% observed binary fraction). This has been taken as evidence for the in-situ formation of cold classicals. Interestingly, a small fraction (~10%) of cold classicals is less red with s<17%, and these "blue" bodies are often found in wide binaries. Here we study the dynamical implantation of blue binaries from r<42 au. We find that they can be implanted into the cold classical belt from a wide range of initial radial distances, but the survival of the widest blue binaries -- 2001 QW322 and 2003 UN284 -- implies formation at r>30 au. This would be consistent with the hypothesized less-red to very-red transition at 30<r<40 au. For any reasonable choice of parameters (Neptune's migration history, initial disk profile, etc.), however, our model predicts a predominance of blue singles, rather than blue binaries, which contradicts existing observations. We suggest that wide blue binaries formed in situ at r=42-47 au and their color reflects early formation in a protoplanetary gas disk. The predominantly VR colors of cold classicals may be related to the production of methanol and other hydrocarbons during the late stages of the disk, when the temperature at 45 au dropped to 20 K and carbon monoxide was hydrogenated.