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有一道这样的数学奥林匹克训练题: 某人最初有256元,和人打赌8次,结果赢4次,输4次,惟有次序随意,若赌金是每一赌的余钱的一半,则最后的结果为:(A)不赢也不输 (B)赢81元 (C)输175元(D)输赢依据输与赢发生的次序而定 如果你没有深入计算,凭估计.你可能选择(A)或(D),因为输赢的次数相等.故可能不赢也不输,或由于输赢次序不定,故也可能输赢与次序有关.但结果怎样呢?我们不妨算一算. 设αi为第i次赌前某君手中的赌金,这样
There is such a mathematical Olympics training question: Someone initially had 256 yuan, and people bet 8 times. The result was 4 wins and 4 losses. The order was arbitrary. If the bet was half of the remaining money for each bet, then the last The result is: (A) No wins or loses (B) Wins 81 yuan (C) Wins 175 yuan (D) Wins or loses depends on the order in which wins and losses occur. If you do not make in-depth calculations, based on estimates, you may choose ( A) or (D), because the number of wins and losses is equal, it may not win nor lose, or because of the order of winning or losing, it may also be related to the order of winning or losing. But what is the result? We may have to count. Let αi be the first i bet on a bet in front of a monarch, so