Did Jesus lie about going to a feast?

I know Jesus is not a liar, but an incident in the New Testament has puzzled me for a long time. Jesus was asked by his disciples if he was going to go to a feast and he said he wasn't, but, later he went: >You go up to the feast. I am not going up to this feast, for my time has not yet fully come. (John 7:8, ESV) > >But after his brothers had gone up to the feast, then he also went up, not publicly but in private. (7:10) Could someone explain this contradiction?