The beavers and dogs had a competition. In total nine animals took part.
海狸和狗举行了一场竞赛。总共有九只动物参加。
The nine participants had the following scores: 1, 2, 2, 3, 4, 5, 5, 6, 7.
九位参赛者的得分如下：1 分、2 分、2 分、3 分、4 分、5 分、5 分、6 分、7 分。
No dog scored more than any beaver.
没有狗的得分超过任何一只海狸。
One dog had a tie with a beaver.
有一只狗和一只海狸结伴而行。
There were also two other dogs that had a tie with each other.
还有另外两只狗彼此关系也很亲密。
Question: 问题:
How many dogs took part in the competition?有多少只狗参加了比赛？
A. 2
B. 3
C. 5
D. 6
E. 7
Explanation 解释
The answer D (6) is correct.
答案 D（6）是正确的。
If no dog scored more than any beaver, we can order animals in a row so that a border could be laid between dogs and beavers.
如果没有任何一只狗的得分高于任何一只海狸，那么我们就可以将动物们排成一排，从而在狗和海狸之间划出一条分界线。
Example: dogs1, 2, 2, 3, | 4, 5, 5, 6, 7 beavers , where "|" means border between dogs and beavers.
示例：<b0></b0>；1、2、2、3、| 4、5、5、6、7 <b1></b1>；，其中“|”表示狗和海狸之间的分界线。
Because one dog scored same as one beaver and there are two pairs of the same value in the row: 2, 2 and 5, 5, some dog must have scored 2 or 5 (and of course some beaver too).
因为一只狗的得分与一只海狸相同，而且这一行中有两对相同的数字：2 和 2 以及 5 和 5，所以一定有一只狗得分为 2 或 5（当然也有一只海狸得同样的分）。
If 2, 2 would be a border between dogs and beavers, two dogs must have scored 5, 5 and then they will be better than the beaver that scored 2. This is in contradiction with the task settings.
如果 2、2 是狗和海狸之间的分界线，那么两只狗的得分必须是 5、5，这样它们就会比得分为 2 的海狸更好。这与任务设定相矛盾。
So the dog and the beaver with the same score must have score 5, and the border between dogs and beavers must be between 5 | 5:
所以得分相同的狗和海狸的得分一定是 5 分，狗和海狸之间的分界线一定在 5 | 5 之间：
dogs 1, 2, 2, 3, 4, 5, | 5, 6, 7 beavers.
6 dogs participated in a competition.
6 只狗参加了一场比赛。
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