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I remember this book, but I've forgotten the title. I remember it as him figuring it out when his best friend scratched up his arm, showing the dark skin below the makeup. The "every third word" bit rings true too. *wry grin* Just figured I'd let you know you're not crazy, that someone else has read it.
I've definatly read it, but I can't remember the name of it either. From what I can recall, it strikes me as being similar in style and tone to a lot of Poul Anderson 's works, but after looking over a list of his books I can't find it. I am fairly certain it is from the 60's or 70's though.
That's Piers Anthony's Race Against Time. Something of an Old Shame for Anthony, as it was meant to be a Twilight Zone-ish kids' suspense story, but wound up having Unfortunate Implications of being against miscegenation.

When I was younger I read this book that was about these people who seemed to be the last of their race. It was from the perspective of a male, and he had a penpal who was the last female of his race. He found out that everyone around them just used makeup to make themselves look like they were of the same race. He first realized something was amiss when his dog climbed a tree, so he wrote the girl and tried to put it in code (every third word), but when she replied she just told him flatout that they were the last ones. They ended up running away and using the makeup to look like most people, and went to go find the other people who were the last of their race. One thing though, it never actually refers to it as "race" just colour. So he is white, and he goes to find the yellow people. I think they end up on a spaceship or something, but I don't remember. I've wanted to find this book for years. Its from the early '90s or before. I can't think of any other info that would help, but if someone knows what this is, I would be ever so grateful.