All the puzzles, all the solutions

You’ll need to make 7 trips.

1. Take the hen over.
2. Return.
3. Take the corn over.
4. Return with the hen.
5. Take the fox over.
6. Return.
7. Take the hen over.

Turn the first switch on for 5 minutes, then switch on the second and enter the room. If the bulb is on, it’s controlled by the 2nd switch. If the bulb is off but it’s warm to the touch, the 1st switch controls the bulb. If the bulb is off but it’s not warm, the 3rd switch controls the bulb.

Start and finish at the only intersections with an odd number of paths. To travel through one intersection to another you need an entrance and exit point. Some intersections have two (which you travel through once), some have four (which you travel through twice). The intersections that don’t are the two that don’t need an entrance (the start) or an exit (the finish). Once you know that, there are many ways to traverse the trail without using the same path twice or missing any intersections.

Ask one of the guards, ‘Which door would the other guard say leads to triumph?’ If you ask the guard who tells the truth, he knows the other guard would lie, and point to the door leading to disaster. If you ask the guard who lies, he knows the other guard would tell the truth, so he’ll lie and also point you to the door leading to disaster. So, you simply chose the other door.