巧分食盐水问题

  • 时间:2020-06-22 16:00:25
  • 分类:数学世界
  • 阅读:109 次

数学百题之八:巧分食盐水问题。大家在常识课上认识了量杯。快下课时,王老师让我们用手中的量杯做
一个智力小游戏:有30 毫升、70 毫升、100 毫升的量杯各1 个,请你用这三个量杯把水槽中的100 毫升食盐水平均分成两份,但分的时候不准看量杯的刻度。大家动手试一试,至少要分几次才成?

分析与解:至少分9 次。这种题,一般统称为分液问题。解答时,最好用列表的方法。本题解答方法,如下表所示(这不是唯一的方法):

杯子容量100 毫升70 毫升30 毫升(下面是分的过程中各杯子中水的体积)
1 30 70 0
2 30 40 30
3 60 40 0
4 60 10 30
5 90 10 0
6 90 0 10
7 20 70 10
8 20 50 30
9 50 50 0

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