Este é um tiro longo, mas a cena com um carrossel aparece em Merry Go Round em Oz por Eloise Jarvis McGraw e Lauren McGraw Wagner. Isto foi publicado em 1963, para que se adapte ao seu calendário. No entanto, é apenas o protagonista, Robin, montando o carrossel não um grupo de crianças e é um anel de latão não um anel de ouro.
The little man had certainly vanished-probably, thought Robin, he was on the other side of the merry-go-round selling tickets to someone else. For the first time, he examined his own ticket, and found that it 'was a curious one, as he had thought. It was as large as a postcard, and scarlet, like the mare. Across one side of it in shining gilt letters was printed: GRAB THE BRASS RING FOR A FREE RIDE
...
After the fourth or fifth failure, Robin began to grow stubborn, as he always did when he failed at something. Then he grew ingenious, as he always did when he became stubborn. While his little red mare was leaping and bounding around the rest of the circle, he prepared hastily for the moment at which he would pass that tantalizing metal arm again. With some difficulty, since the merry-go-round was now whirling at top speed and his mare was very spirited, he stood up in his stirrups, wound his left arm tightly around the mare's pole to brace himself, and leaned perilously far out, with his right arm stretched full length.
Now! Here came the arm again-why, there was the little man, standing right under it, stamping one foot and shouting as he stamped. Reach, Sonny! Reach! Reach! Reach! Reach!"
"I'm t-trying-" Robin panted, reaching with all his might . . .Click! "I got it, I got it!" Robin shouted, holding the ring high. He had one swift glimpse of the little man throwing his hat triumphantly in the air, then-CRACK!!!!
O CRACK !!!! é claro que o anel o transporta para Oz.
Para completar, vou gravar os outros dois livros identificados nos comentários:
The detail about waking up by banging your head on the pillow appears in chapter 4 of Five Children and It by E. Nesbit. Identified by ssav.
The room with the portal-windows is in The Swing in the Summerhouse by Jane Langton. This book is the sequel to The Diamond in the Window. Identified by OP.