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我校毕业班数学竞赛,出了下面这道试题: 梨若干个,将梨的一半又1个给甲,次将余下的一半又1个给乙,再取剩下的一半又3个给丙,这样梨恰好分完。求梨总数是多少个? 参赛者有的用画线段图的方法解,有的用整体“1”来解,有的用分数解,有的用倍数解,最终均由于繁难或解题思路受阻甚至理不清头绪而未获得圆满成功。其实,这类题可用“倒推法”(即“剥笋法”)巧解。 所谓“倒推法”(“剥笋法”)就是从最后一个条件入手,层层反剥、倒推,从而解答问题。
My school graduation class math contest, out of the following questions: Pear number, the pear half and one to A, the second half and a second to B, and then take the remaining half and three to C , So pear exactly finished points. The total number of pear is how many? The contestants, some with the method of drawing line diagram solution, and some with the overall “1” to solve, and some with fractional solution, and some with multiple solutions, and ultimately due to difficult or problem-solving ideas blocked Not even clueless but not a complete success. In fact, these questions can be used “push back law” (that is, “peeled bamboo shoot method”) cleverly solved. The so-called “push-back method” (“pecking-bamboo law”) is to start from the last condition, layers of anti-stripping, backlash, to answer the question.