Brain Teasers
The Troll Bridge 1
A bridge was guarded by an evil troll. The troll was very intelligent, but he was also a coward. He was afraid of anyone smarter than him. So every time anyone tried to cross the bridge, the troll would set up a test. If the traveler passed the test, he would be allowed to cross. Otherwise, the troll would eat him.
Three travelers, Al, Ben and Carl, came across the bridge. The troll told them, "You may only cross my bridge if you know the password." He wrote five three-letter words on a rock. The five words were HOE, OAR, PAD, TOE, and VAT.
He then said, "I will tell each of you a different letter from the password. If you know what the password is, I will let you pass. But don't tell anyone else your letter." He then whispered a letter from the password to each traveler so that neither of the other two could hear him.
Then the troll asked Al, "Do you know what the password is?" "Yes," said Al, and the troll let him pass.
Then the troll asked Ben, "Do you know what the password is?" "Yes," said Ben, and the troll let him pass.
Then the troll asked Carl, "Do you know what the password is?" "Yes," said Carl, and the troll let him pass.
So, what is the password?
Three travelers, Al, Ben and Carl, came across the bridge. The troll told them, "You may only cross my bridge if you know the password." He wrote five three-letter words on a rock. The five words were HOE, OAR, PAD, TOE, and VAT.
He then said, "I will tell each of you a different letter from the password. If you know what the password is, I will let you pass. But don't tell anyone else your letter." He then whispered a letter from the password to each traveler so that neither of the other two could hear him.
Then the troll asked Al, "Do you know what the password is?" "Yes," said Al, and the troll let him pass.
Then the troll asked Ben, "Do you know what the password is?" "Yes," said Ben, and the troll let him pass.
Then the troll asked Carl, "Do you know what the password is?" "Yes," said Carl, and the troll let him pass.
So, what is the password?
Hint
1. Ben used Al's answer, and Carl used both Al's and Ben's answers.2. Al's letter could not have been E.
Answer
The password was HOE.The only letters unique to one of the five words were D, H, P, R, and V. One of these letters must have been Al's, since he could determine the password. The only word without any of these letters is TOE. So the password could not have been TOE.
Ben knew this and now had four words to think of. The only letters unique to one word were D, E, H, P, R, T, and V. The password must have contained at least two unique letters, one for Al and the other for Ben, since they were both able to determine the password. The only word with only one of these letters was OAR. So OAR could not have been the password.
Carl knew this and now had three words to think of. The only letters unique to one word were D, E, H, O, P, T, and V. The password must have included three of these letters, since all three were able to determine the password. The only one of the three words containing three such letters was HOE, so this must have been the password.
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