Sisneroz

But remember, the lab assistant has been waiting on the other side,and she's the second fastest of the group.So she grabs the lantern from the professor and runs back across to you.Now with only two minutes left,the two of you make the final crossing.As you step on the far side of the gorge,you cut the ropes and collapse the bridge behind you,just in the nick of time.Maybe next summer, you'll just stick to the library.

Only three minutes have passed.So far, so good.Now comes the hard part.The professor and the janitor take the lantern and cross together.This takes them ten minutes since the janitor has to slow down for the old professor who keeps muttering that he probably shouldn't have given the zombies night vision.By the time they're across,there are only four minutes left,and you're still stuck on the wrong side of the bridge.

The key is to minimize the time wasted by the two slowest people by having them cross together.And because you'll need to make a couple of return trips with the lantern,you'll want to have the fastest people available to do so.So, you and the lab assistant quickly run across with the lantern,though you have to slow down a bit to match her pace.After two minutes, both of you are across,and you, as the quickest, run back with the lantern.

Most importantly, everyone must be safely across before the zombies arrive.Otherwise, the first zombie could step on the bridge while people are still on it.Finally, there are no tricks to use here.You can't swing across,use the bridge as a raft,or befriend the zombies.Pause the video now if you want to figure it out for yourself!Answer in: 3Answer in: 2Answer in: 1At first it might seem like no matter what you do,you're just a minute or two short of time,but there is a way.

Unfortunately, the bridge can only hold two people at a time.To make matters worse,it's so dark out that you can barely see,and the old lantern you grabbed on your way only illuminates a tiny area.Can you figure out a way to have everyone escape in time?Remember: no more than two people can cross the bridge together,anyone crossing must either hold the lantern or stay right next to it,and any of you can safely wait in the dark on either side of the gorge.

You can dash across in a minute,while the lab assistant takes two minutes.The janitor is a bit slower and needs five minutes,and the professor takes a whole ten minutes,holding onto the ropes every step of the way.By the professor's calculations,the zombies will catch up to you in just over 17 minutes,so you only have that much time to get everyone across and cut the ropes.

She gives him 45 kiloliters of her remaining 90,leaving them with 45 each.But that's just half of what they need to make it to the airport.Fortunately, this is exactly when Fugōri,having refueled, takes off.45 minutes later, just as the other two planes are about to run empty,he meets them at the 315 degree point and transfers 45 kiloliters of fuel to each, leaving 45 for himself.All three planes land at the airport just as their fuel gauges reach zero.As the reporters and photographers cheer,the professor promises his planes will soon be available for commercial flights,just as soon as they figure out how to keep their inflight meals from spilling everywhere.

Professor Fukanō stretches and puts on his favorite album.He'll be alone for a while.In the meantime, Orokana has been anxiously awaiting Fugōri's return,her plane fully refueled and ready to go.As soon as his plane touches the ground,she takes off, this time flying east.At this point, exactly 180 minutes have passed and the professor is at the halfway point of his journey with 90 kiloliters of fuel left.For the next 90 minutes,the professor and Orokana's planes fly towards each other,meeting at the three-quarter mark.Just as the professor's fuel is about the run out, he sees Orokana's plane.

After 45 minutes, or one-eighth of the way around,each plane has 135 kiloliters left.Orokana gives 45 to the professor and 45 to Fugōri,fully refueling them both.With her remaining 45, Orokana returns to the airport and heads to the lounge for a well-deserved break.45 minutes later, with one-quarter of the trip complete,the professor and Fugōri are both at 135 kiloliters again.Fugōri transfers 45 into the professor's tank,leaving himself with the 90 he needs to return.

According to the professor's calculations,they should be able to pull it off by a hair.The key is to maximize the support each assistant provides,not wasting a single kiloliter of fuel.It also helps us to think symmetrically so they can make shorter trips in either direction while setting the professor up for a long unsupported stretch in the middle.Here's his solution.All three planes take off at noon flying west,each fully loaded with 180 kiloliters.After 45 minutes, or one-eighth of the way around,each plane has 135 kiloliters left.

However, only one airport,located on the equator,has granted permission for the experiment,making it the starting point,the finish line,and the only spot where the planes can land,takeoff,or refuel on the ground.How should the three planes coordinate so the professor can fly continuously for the whole trip and achieve his dream without anyone running out of fuel and crashing?Pause here if you want to figure it out for yourself.

Instead, he's devised a slightly more elaborate solution:building three identical planes for the mission.In addition to their speed,the professor's equipped them with a few other incredible features.Each of the planes can turn on a dime and instantly transfer any amount of its fuel to any of the others in midair without slowing down,provided they're next to each other.The professor will pilot the first plane,while his two assistants Fugōri and Orokana will pilot each of the others.

Professor Fukanō, the famous eccentric scientist and adventurer,has embarked on a new challenge:flying around the world nonstop in a plane of his own design.Able to travel consistently at the incredible speed of one degree longitude around the equator per minute,the plane would take six hours to circle the world.There's just one problem:the plane can only hold 180 kiloliters of fuel,only enough for exactly half the journey.Let's be honest.The professor probably could have designed the plane to hold more fuel,but where's the fun in that?

So you could throw a bunch of Reuleaux tetrahedra on the floor,and slide a board across them as smoothly as if they were marbles.Now back to manhole covers.A square manhole cover's short edge could line up with the wider part of the hole and fall right in.But a curve of constant width won't fall in any orientation.Usually they're circular, but keep your eyes open,and you just might come across a Reuleaux triangle manhole.

In three dimensions, we can make surfaces of constant width,like the Reuleaux tetrahedron,formed by taking a tetrahedron,expanding a sphere from each vertex until it touches the opposite vertices,and throwing everything away except the region where they overlap.Surfaces of constant width maintain a constant distance between two parallel planes.

For example, if you roll any curve of constant width around another,you'll make a third one.This collection of pointy curves fascinates mathematicians.They've given us Barbier's theorem,which says that the perimeter of any curve of constant width,not just a circle,equals pi times the diameter.Another theorem tells us that if you had a bunch of curves of constant width with the same width,they would all have the same perimeter,but the Reuleaux triangle would have the smallest area.The circle, which is effectively a Reuleaux polygon with an infinite number of sides,has the largest.

Because Reuleaux triangles can rotate between parallel lines without changing their distance,they can work as wheels,provided a little creative engineering.And if you rotate one while rolling its midpoint in a nearly circular path,its perimeter traces out a square with rounded corners,allowing triangular drill bits to carve out square holes.Any polygon with an odd number of sides can be used to generate a curve of constant width using the same method we applied earlier,though there are many others that aren't made in this way.

This makes the circle unlike the square,a mathematical shape called a curve of constant width.Another shape with this property is the Reuleaux triangle.To create one, start with an equilateral triangle,then make one of the vertices the center of a circle that touches the other two.Draw two more circles in the same way,centered on the other two vertices,and there it is, in the space where they all overlap.

Why are most manhole covers round?Sure, it makes them easy to roll and slide into place in any alignment but there's another more compelling reason involving a peculiar geometric property of circles and other shapes.Imagine a square separating two parallel lines.As it rotates, the lines first push apart,then come back together.But try this with a circle and the lines stay exactly the same distance apart,the diameter of the circle.