Riddle
The beavers and dogs had a competition. In total nine animals took part. The nine participants had the following scores: 1, 2, 2, 3, 4, 5, 5, 6, 7. No dog scored more than any beaver. One dog tied with a beaver. There were also two other dogs that tied with each other.
Question:
How many dogs took part in the competition?
Top answer
There are three keys to this, the two ties, dog-dog and dog-beaver (these have to be the scores 2-2 and 5-5), the fact that no dog can have a higher score than a beaver, and the fact that the nine given scores are, conveniently for us, in ascending value (this means that in the dog-beaver tie, the right score, the higher one, has to be the beaver's). Right away, we see that the dog-beaver tie has to be the 5-5, which leaves the 2-2 as the dog-dog tie. The 2-2 can't be the dog-beaver tie because then the 5-5 would have to be the dog-dog, which would put a dog score higher than a beaver.
- There are three keys to this, the two ties, dog-dog and dog-beaver (these have to be the scores 2-2 and 5-5), the fact that no dog can have a higher score than a beaver, and the fact that the nine given scores are, conveniently for us, in ascending value (this means that in the dog-beaver tie, the right score, the higher one, has to be the beaver's).
- Right away, we see that the dog-beaver tie has to be the 5-5, which leaves the 2-2 as the dog-dog tie.
- The 2-2 can't be the dog-beaver tie because then the 5-5 would have to be the dog-dog, which would put a dog score higher than a beaver.
- Then, 1, 3, and 4 have to be dog scores, since the left 5 score is a dog and no dog can have a higher score than a beaver.
- And then 6 and 7 have to be beaver scores, since the right 5 score is a beaver and no dog can score higher than a beaver.
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There are three keys to this, the two ties, dog-dog and dog-beaver (these have to be the scores 2-2 and 5-5), the fact that no dog can have a higher score than a beaver, and the fact that the nine given scores are, conveniently for us, in ascending value (this means that in the dog-beaver tie, the right score, the higher one, has to be the beaver's).
Right away, we see that the dog-
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