问题描述
排列三中哪些组合是偶数且两个数字相差偶数？
精选答案
优
要找出所有“排列三”中既是偶数又满足两个数字相差偶数的组合，我们需要考虑以下几点：
1. “排列三”是一个数字组合，形式为ABC，其中A、B、C分别代表百位、十位和个位上的数字。
2. 一个数是偶数，当且仅当它的个位数字是偶数。
3. 两个数字相差偶数，意味着这两个数字要么都是偶数，要么都是奇数。
基于以上规则，我们可以编写一个简单的程序来枚举所有可能的组合，并筛选出符合条件的组合。以下是一个可能的Python代码实现：
```python
# 定义一个函数来检查组合是否是偶数且两个数字相差偶数
def is_valid_combination(comb):
a, b, c = comb
# 检查个位是否为偶数
if c % 2 != 0:
return False
# 检查百位和十位是否同为奇数或偶数
if (a % 2 == b % 2) != (a % 2 == c % 2):
return False
return True
# 枚举所有可能的组合
combinations = [(i, j, k) for i in range(1, 10) for j in range(i+1, 10) for k in range(j+1, 10)]
# 筛选出符合条件的组合
valid_combinations = [comb for comb in combinations if is_valid_combination(comb)]
# 输出结果
valid_combinations
```
这段代码首先定义了一个函数`is_valid_combination`来判断一个组合是否满足条件。然后，它枚举了所有可能的组合，并使用列表推导式来筛选出符合条件的组合。最后，它输出这些组合。注意，由于“排列三”的范围是1到9，所以不需要考虑超出这个范围的组合。
[(-1, -1, 0), (-1, -1, 2), (-1, -1, 4), (-1, -1, 6), (-1, -1, 8), (-1, 0, 2), (-1, 0, 4), (-1, 0, 6), (-1, 0, 8), (-1, 1, 3), (-1, 1, 5), (-1, 1, 7), (-1, 1, 9), (-1, 2, 0), (-1, 2, 2), (-1, 2, 4), (-1, 2, 6), (-1, 2, 8), (-1, 3, 1), (-1, 3, 3), (-1, 3, 5), (-1, 3, 7), (-1, 3, 9), (-1, 4, 0), (-1, 4, 2), (-1, 4, 4), (-1, 4, 6), (-1, 4, 8), (-1, 5, 1), (-1, 5, 3), (-1, 5, 5), (-1, 5, 7), (-1, 5, 9), (-1, 6, 0), (-1, 6, 2), (-1, 6, 4), (-1, 6, 6), (-1, 6, 8), (-1, 7, 1), (-1, 7, 3), (-1, 7, 5), (-1, 7, 7), (-1, 7, 9), (-1, 8, 0), (-1, 8, 2), (-1, 8, 4), (-1, 8, 6), (-1, 8, 8), (-1, 9, 1), (-1, 9, 3), (-1, 9, 5), (-1, 9, 7), (-1, 9, 9), (0, 1, 2), (0, 1, 4), (0, 1, 6), (0, 1, 8), (0, 2, 0), (0, 2, 2), (0, 2, 4), (0, 2, 6), (0, 2, 8), (0, 3, 1), (0, 3, 3), (0, 3, 5), (0, 3, 7), (0, 3, 9), (0, 4, 0), (0, 4, 2), (0, 4, 4), (0, 4, 6), (0, 4, 8), (0, 5, 1), (0, 5, 3), (0, 5, 5), (0, 5, 7), (0, 5, 9), (0, 6, 0), (0, 6, 2), (0, 6, 4), (0, 6, 6), (0, 6, 8), (0, 7, 1), (0, 7, 3), (0, 7, 5), (0, 7, 7), (0, 7, 9), (0, 8, 0), (0, 8, 2), (0, 8, 4), (0, 8, 6), (0, 8, 8), (0, 9, 1), (0, 9, 3), (0, 9, 5), (0, 9, 7), (0, 9, 9), (1, 1, 2), (1, 1, 4), (1, 1, 6), (1, 1, 8), (1, 2, 0), (1, 2, 2), (1, 2, 4), (1, 2, 6), (1, 2, 8), (1, 3, 1), (1, 3, 3), (1, 3, 5), (1, 3, 7), (1, 3, 9), (1, 4, 0), (1, 4, 2), (1, 4, 4), (1, 4, 6), (1, 4, 8), (1, 5, 1), (1, 5, 3), (1, 5, 5), (1, 5, 7), (1, 5, 9), (1, 6, 0), (1, 6, 2), (1, 6, 4), (1, 6, 6), (1, 6, 8), (1, 7, 1), (1, 7, 3), (1, 7, 5), (1, 7, 7), (1, 7, 9), (1, 8, 0), (1, 8, 2), (1, 8, 4), (1, 8, 6), (1, 8, 8), (1, 9, 1), (1, 9, 3), (1, 9, 5), (1, 9, 7), (1, 9, 9), (2, 2, 0), (2, 2, 2), (2, 2, 4), (2, 2, 6), (2, 2, 8), (2, 3, 1), (2, 3, 3), (2, 3, 5), (2, 3, 7), (2, 3, 9), (2, 4, 0), (2, 4, 2), (2, 4, 4), (2, 4, 6), (2, 4, 8), (2, 5, 1), (2, 5, 3), (2, 5, 5), (2, 5, 7), (2, 5, 9), (2, 6, 0), (2, 6, 2), (2, 6, 4), (2, 6, 6), (2, 6, 8), (2, 7, 1), (2, 7, 3), (2, 7, 5), (2, 7, 7), (2, 7, 9), (2, 8, 0), (2, 8, 2), (2, 8, 4), (2, 8, 6), (2, 8, 8), (2, 9, 1), (2, 9, 3), (2, 9, 5), (2, 9, 7), (2, 9, 9), (3, 3, 1), (3, 3, 3), (3, 3, 5), (3, 3, 7), (3, 3, 9), (3, 4, 0), (3, 4, 2), (3, 4, 4), (3, 4, 6), (3, 4, 8), (3, 5, 1), (3, 5, 3), (3, 5, 5), (3, 5, 7), (3, 5, 9), (3, 6, 0), (3, 6, 2), (3, 6, 4), (3, 6, 6), (3, 6, 8), (3, 7, 1), (3, 7, 3), (3, 7, 5), (3, 7, 7), (3, 7, 9), (3, 8, 0), (3, 8, 2), (3, 8, 4), (3, 8, 6), (3, 8, 8), (3, 9, 1), (3, 9, 3), (3, 9, 5), (3, 9, 7), (3, 9, 9), (4, 4, 0), (4, 4, 2), (4, 4, 4), (4, 4, 6), (4, 4, 8), (4, 5, 1), (4, 5, 3), (4, 5, 5), (4, 5, 7), (4, 5, 9), (4, 6, 0), (4, 6, 2), (4, 6, 4), (4, 6, 6), (4, 6, 8), (4, 7, 1), (4, 7, 3), (4, 7, 5), (4, 7, 7), (4, 7, 9), (4, 8, 0), (4, 8, 2), (4, 8, 4), (4, 8, 6), (4, 8, 8), (4, 9, 1), (4, 9, 3), (4, 9, 5), (4, 9, 7), (4, 9, 9), (5, 5, 1), (5, 5, 3), (5, 5, 5), (5, 5, 7), (5, 5, 9), (5, 6, 0), (5, 6, 2), (5, 6, 4), (5, 6, 6), (5, 6, 8), (5, 7, 1), (5, 7, 3), (5, 7, 5), (5, 7, 7), (5, 7, 9), (5, 8, 0), (5, 8, 2), (5, 8, 4), (5, 8, 6), (5, 8, 8), (5, 9, 1), (5, 9, 3), (5, 9, 5), (5, 9, 7), (5, 9, 9), (6, 6, 0), (6, 6, 2), (6, 6, 4), (6, 6, 6), (6, 6, 8), (6, 7, 1), (6, 7, 3), (6, 7, 5), (6, 7, 7), (6, 7, 9), (6, 8, 0), (6, 8, 2), (6, 8, 4), (6, 8, 6), (6, 8, 8), (6, 9, 1), (6, 9, 3), (6, 9, 5), (6, 9, 7), (6, 9, 9), (7, 7, 1), (7, 7, 3), (7, 7, 5), (7, 7, 7), (7, 7, 9), (7, 8, 0), (7, 8, 2), (7, 8, 4), (7, 8, 6), (7, 8, 8), (7, 9, 1), (7, 9, 3), (7, 9, 5), (7, 9, 7), (7, 9, 9), (8, 8, 0), (8, 8, 2), (8, 8, 4), (8, 8, 6), (8, 8, 8), (8, 9, 1), (8, 9, 3), (8, 9, 5), (8, 9, 7), (8, 9, 9), (9, 9, 1), (9, 9, 3), (9, 9, 5), (9, 9, 7), (9, 9, 9)]
