What month did April and Melanie start "The Egypt Game"?

April and
Melanie get the idea for the Egypt Game during the time they spend in the library in August. 
They begin the game itself "in September, in the Professor's deserted
yard".

It is August when April arrives at the Casa Rosada to live with
her grandmother.  She is befriended by Melanie, and the two girls spend the month "together
almost every day".  They pass the time playing games, take Melanie's little brother for
walks and to the park, and "almost every day they (go) to the library".  One day,
April finds a new book about Egypt at the library, "an especially interesting one about the
life of a young pharaoh".  She passes it on to Melanie, and soon, the two girls, "with
the help of a sympathetic librarian...(have) found and read just about everything the library
(has) to offer on Egypt".  April and Melanie begin to devise their own system of
hieroglyphics, and they become known at the library as "the Egypt
Girls".

At the beginning of September, "with school only a few days
away", the girls discover the Professor's backyard, and the Egypt Game begins (Chapter 4). 
Other people are accepted in the group, and the game grows and develops through the fall until
unforeseen circumstances involving the Professor intervene.  When the situation is resolved just
after Christmas, the girls decide the game has run its course, and begin to share ideas for new
adventures.