Two cubes each has 6 sides, which represents 1, 2, 3, 4, 5, 6 respectively. Put the two cubes on the desk, how many possibilitie

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问题 Two cubes each has 6 sides, which represents 1, 2, 3, 4, 5, 6 respectively. Put the two cubes on the desk, how many possibilities are there that the sum of the numbers on the two upsides is even?

选项 A、9
B、6
C、18
D、24
E、12

答案C

解析偶数：偶数+偶数=奇数+奇数，根据奇数+奇数：偶数，从1，3，5任取两个数和为偶数，有C₃²=3种，由于1+3：3+1，第一个立方体的面值为1，第二个立方体的面值为3和第一个立方体的面值为3，第二个立方体的面值为1要算作两种情况，所以面值为奇数有3×2=6种。
同理：偶数+偶数=偶数，2，4，6任取两个数和为偶数，面值取偶数也有C₃²×2=6种。
有些考生到此认为刚好是6+6=12种可能，选择E，但其实疏忽了最重要的一点，因为两个1，两个2……两个6相加的和都是偶数，所以还有面值相等的6种可能，前面所讲的都是面值不等的情况，所以一共有12+6=18种可能。

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