A wilderness guide is escorting a college professor and one of his students through a remote jungle. The student, as always, has brought along his Xbox. Suddenly, the group encounters a pack of savage, man-eating tigers. Knowing that savage, man-eating tigers cannot cross rivers, the guide quickly tosses the group's lunch to distract the tigers and rushes everyone to the nearby river. While the food will keep the tigers occupied for a short while, the group will be eaten if they do not cross the river quickly. They made a plan.

Rules:

2. There is a small canoe at the river that can carry just two people or items at a time
4. Only the guide is skilled enough to maneuver the canoe across the river and back
6. If the student is alone with the Xbox, he will obsessively play it and will have to be left behind (where he will meet certain death)
8. If the professor is alone with the student, he will uncontrollably lecture on obscure jungle-related topics and will have to be left behind (where he will also meet certain death)
10. Don't ask silly questions like "How does the student play Xbox in the middle of the jungle while running away from savage, man-eating tigers?" The student possesses a self-contained, solar-powered Xbox.

Question 1:

If we represent each of the party as: the Guide (Gu), the Professor (Pr), the Student (St), and the Xbox (Xb), what/who needs to be the first carried across the river with the guide?

Question 2:

According to the puzzle, certain combinations of people/items are not allowed. For exampleL[Gu, Pr, St] - R[Xb]is ok because it doesn't violate any of the rules.

How many illegal states (combinations) are possible for this puzzle?

Question 3:

What is the minimum number of steps (crossings) to get the entire party across the river to avoid the man-eating tigers?

Part 2 - Crossing the Bridge

Having narrowly escaped the savage, man-eating tigers, the guide, professor and student have met up with the professor's teaching assistant deep inside a cave. After several hours of adventuring, all the flashlights except for the guide's lantern have run out of power.

Tired of being in the dark (and not being able to play his solar-powered Xbox), the student lights a candle on the wall. Upon closer inspection, the student is dismayed to learn that the candle is, in fact, a bundle of dynamite! The group fails repeatedly to put it out and realise if they don't escape quickly, they will be trapped when the dynamite brings down the cave around them. The group has 20 minutes to escape.

They are now close to the cave entrance, except that between them and the entrance is a large and VERY deep gorge with nothing but an ancient and quite sketchy foot rope bridge to cross on, and they each know how long it took them to cross on the way in. Once they are over the bridge they can be out of the cave, and safe, in 3 minutes.

Rules:

2. The bridge can only support two people at a time
4. The only way to cross the bridge safely is with the lantern
6. The guide is accustomed to these kinds of bridges, so it only takes him 1 minute to cross
8. The teaching assistant used to be a navy seal, so it takes him 2 minutes to cross
10. The professor isn't terribly steady on the bridge, so it takes him 6 minutes to cross
12. The only bridge the student ever crossed was a virtual one on his Xbox, so it takes him 10 minutes to cross
14. If two people cross together, it takes the time of the slower person to get across (sharing the lantern light)
16. They must all be on the far side of the bridge in 17 minutes or less

Question 4:

Is it possible to get everyone across? If so say True, otherwise say False. Note that there are obviously no second chances for True/False questions, so make sure you figure out the right answer first time. Be prepared!