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# Logic Problems to Challenge Your Bored Brain

## They’ll make the time pass lightning fast.

Popular Science

Read when you’ve got time to spare.

Can you solve these logic problems? Photo by Pexels

There’s nothing more painful than watching the time pass. Instead, occupy your mind with these logic problems. Then whip them out on video chats and socially-distant hangs, and watch your friends scratch their heads. Answers are below each question, but don’t cheat!

## Time Trials

Q: A kindergartner, a fifth grader, a high school track star, and an Olympic sprinter are all waiting in line at a track-and-field meet’s food stand. Suddenly, the storm of the century starts to roll in. The only way back to the safety of the stadium is across a wobbly bridge in critical need of repair. The rickety old thing can handle only two people crossing at one time. Three runners or even a strong burst of wind could knock it away entirely. To make matters worse, the tempest’s dark clouds have blotted out the sun completely. Luckily, the kindergartner has a flashlight keychain attached to his backpack that provides just enough light to travel across safely.

The winds that will take down the structure begin in 17 minutes. The Olympic sprinter can race across in just one minute, and the high school track runner can manage in two. But it takes the fifth grader a plodding five minutes and the kindergartner an even slower 10. Given that the dilapidated bridge can handle just two people at once and one of the travelers must always have the flashlight in hand, how can the group get to safety in the allotted time?

Hint: The Olympian crosses the bridge three times.

A: The Olympic sprinter and the high school track star cross together first (two minutes). The Olympic sprinter rushes back, light in hand (one minute). Then, the fifth grader and the kindergartner run across, with the light (10 minutes). The high school track star, waiting on the other side, rushes back with the flashlight to grab the Olympian (two minutes). Together, they run across just before the bridge collapses (two minutes, for a total of 17 minutes).

## A calculated trip

Q: An amateur engineer plans to circumnavigate the equator in an airplane he ­designed himself. Unfortunately, when he built it, he hadn’t planned on using it for a flight of this nature. So, the plane holds only enough fuel to make it halfway. Intent on making this feat a reality, he built two more identical planes and convinced his two friends, Jen and Dan, to pilot the spare planes and help him along to achieve his goal. The planes can transfer their fuel midair at any point during the trip, but there’s a catch: Only one airport on Earth will allow these homemade airliners to take off and land—and it ­happens to be located along the way.

The engineer wants to travel the entire globe without stopping, and Jen and Dan have agreed to stop, refuel, and follow the engineer in whatever manner necessary to help. It won’t be easy: Each plane holds 180 gallons of fuel and can travel 1 degree of longitude (it takes 360 degrees to circle the world) in one minute for every 1 gallon of fuel. How can Jen and Dan help? When should they stop, transfer fuel to the engineer, and head to and from the airport?

Hint: Jen and Dan both make one airport pit stop.

A: All three planes take off at the same time and head west for 45 minutes, making it one-eighth of the way there. At that point, Dan gives 45 gallons of his fuel each to Jen and the engineer. Jen and the engineer press on, and Dan returns to the airport. When they reach the 90 degree mark, Jen gives 45 gallons to the engineer and heads back to the airport; the engineer keeps moving. When the engineer hits the 180 degree mark, Dan leaves the airport heading east and meets the engineer at the 270 degree mark. Dan gives him 45 gallons, turns around, and heads west with the engineer. At the same time, Jen heads east to meet them. They all meet again at the 315 degree mark. Jen gives 45 gallons to Dan and the engineer, leaving each plane with 45 gallons—enough to make it back to the airport.

Claire Maldarelli is the Science Editor at Popular Science. She has a particular interest in brain science, the microbiome, and human physiology. Her work has appeared in The New York Times, Scientific American, and Scholastic’s Science World and Super Science magazines, among others. She has a bachelor’s degree in neurobiology from the University of California, Davis and a master’s in science journalism from New York University's Science, Health, and Environmental Reporting Program. Contact the author here.

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