When Cortez arrived in Mexico in A. D. 1519, he observed the inhabitants playing a ceremonial game with a rubber ball. The pre-Columbian inhabitants of Mexico began to use rubber around A. D. 1000. Thus, we can be sure that the game must have originated sometime between approximately A. D. 1000 and Cortez' arrival. The conclusion reached above depends on which one of the following assumptions? ['The game had been played since its inception with a rubber ball.', 'The making of rubber balls was one of the earliest uses of rubber by the inhabitants of Mexico.', 'The pre-Columbian inhabitants of Mexico played games on all ceremonial occasions.', 'The ceremonial game referred to was popular throughout Mexico.']