## Math Puzzles of the Month Asking for Directions

What is the minimum number of questions you need to ask to find your way to this lighthouse?

Lawrence Lee suggested this month’s puzzle. At first glance it appears similar to the To Tell the Truth math puzzle, but upon closer examination it really isn’t. (And that is a hint about how to solve it.)

Off the coast of Seedonia there is a flat, rocky island named Brighton, where only grass and lichen grow. The island is roughly 2 hectares (about 5 acres) in area.

On the island there is only one structure, a 75-meter-tall (246-ft) stone lighthouse.

A tourist on the island wanted to visit the lighthouse and set off down the road. Shortly, he came to a four-way fork and didn’t know which way to turn. But, as the tourist agency had told him in advance, he would find four island residents, each standing by one of the four roads. He could ask them for directions to the lighthouse.

Unfortunately, these people are not all truthful all the time. One always tells the truth. Another always lies.

The third always responds truthfully to the first question asked, but after that will tell the truth if the previous question asked of any of the four was answered truthfully, but lie if the previous question was answered falsely.

The fourth person will always lie in response to the first question asked, but like the third person, will respond to subsequent questions with the same honesty as the person who responded to the previous question the traveler posed.

What is the minimum number of questions you need to ask to find your way to the lighthouse?

Make up some puzzles like these and send them in with your solutions. We’ll post them here in the SEED Science Center.

After you've tried this for yourself, check our solution.