谜底: answer to a riddle...
听: (literary pronunciation, still advocated in Taiwan) to rule, to sentence, to allow...
象棋: Chinese chess...
不得不: have no choice or option but to, cannot but, have to, can't help it, can't avoid...
材料: material, data, makings, stuff...
妒忌: to be jealous of (sb's achievements etc), to be envious, envy...
出人意料: unexpected (idiom), surprising...
秋天: autumn...
根基: foundation...
腐败: corruption, to corrupt, to rot, rotten...