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Brain Teaser: Can you solve the loopy Treasure Hunt problem?

Asked by LostInParadise (31914points) December 30th, 2009

I saw this problem in more abstract form and have tried to make a story out of it.

A friend of yours designs what is to be the world’s most elaborate treasure hunt. This is one of those events where people are given a clue about a certain location and then at each location there is a clue to the next one. The winner is the one who first reaches the final location.

But there is a problem. It becomes apparent that one of the locations points back to a previous one, which will lead people through an interminable loop. The locations and clues are so similar that it is not immediately apparent which location is repeated.

You have been called in to help find which location is repeated. In order to avoid the appearance that something is amiss your friend refuses the simple approach of laying down markers for each visited location. However, if you work with a partner and coordinate your movement through the locations by using a cell phone, it is possible to find the repeated location. How can this be done?

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