I seemed to recall that my son had this book, and as it turns out, he does!
It's called 'The Egypt Game', by Zilpha Keatley Snyder. Copyrighted 1967,
and is a Newbery winner. If this isn't it, I'll be surprised. It's still in
print, as I just bought it a year or two ago.
http://www.amazon.com/Egypt-Game-Yea...6/sr=8-1/qid=1
159026377/ref=pd_bbs_1/104-2587673-0907959?ie=UTF8&s=books