Three fishermen are out fishing together and they each bring their own bucket. The buckets are identical, the only difference is the label on the bucket. The buckets are labeled "Salmon", "Trout", and "Salmon and Trout" and correspond to the fishing preference of each fisherman. Shortly after coming ashore, one of the fishermen realizes that they each put their fish in the wrong bucket when they were fishing, means all three buckets were now labeled incorrectly! Naturally, the lids of the buckets are all closed now.

How many bucket lids need to be opened and how many fish need to be taken out at random in order to properly label the buckets?

A fisherman need to look at only one fish from the bucket labeled "Salmon and Trout". This will lead to one of two outcomes.

**Outcome 1:** If the fish he took is a salmon, it must be the "Salmon" bucket. It cannot be the "Salmon and Trout" bucket since we know the current labels are incorrect and it's not the "Trout" bucket because the fish he took is a salmon. Next, the "Trout" bucket cannot contain only trout since we know the current labels are incorrect, so it must be the "Salmon and Trout" bucket. The remaining bucket, labeled "Salmon", must therefore be the "Trout" bucket.

**Outcome 2:** If the fish he took is a trout, it must be the "Trout" bucket. It cannot be the "Salmon and Trout" bucket since we know the current labels are incorrect and it's not the "Salmon" bucket because the fish he looked at is a trout. Next, the "Salmon" bucket cannot contain only salmon since we know the current labels are incorrect, so it must be the "Salmon and Trout" bucket. The remaining bucket, labeled "Trout" must therefore be the "Salmon" bucket.

There is no comments