1. A family of 4 has the odd task of crossing a dark tunnel with one gas lantern. The problem is that there is only enough gas for the lantern to light for 12 minutes. They cannot travel through the tunnel without the lantern. To add to the trouble, the tunnel is very narrow, and at most 2 family members can go across at a time. Yet another constraint is that each family member takes a different amount of time to cross. Dad takes 1 minute. Mom takes 2 minutes. Older sister takes 4 minutes. Kid brother takes 5 minutes. When 2 people go across, they travel at the speed of the slowest member of the party. How do they all get across before the light goes out?

2. River crossing problems… It will be helpful to use objects to represent the people or things discussed in the following problems. REMEMBER: Boats can’t row themselves!
1. Who hasn’t heard of that lonely farmer trying to get across the river on his lonely boat along with a sheep, a bag of grain, and a fox? “Why the fox?!” you cry in protest. Even though these objects/creatures are completely incidental, let’s at least make an effort to court reality and reasonableness. 
   

2. A new party has arrived at this same confounded river. Originally, this party was said to be made up of 3 missionaries, and 3 cannibals. For reasons of avoiding the racist, imperialist, religious, and unnecessarily controversial implications of this party, we will say that the original reporter had gotten it all wrong. 
   

3. As strange as the zombie tale was, a new party of travelers approaches this bewildering river with even odder restrictions. Fortunately, humanity saved itself against the zombie plague, and society is rebuilding itself. People breathe a sigh of relief now that looming apocalypse has been replaced by the “tolerable” outrages of business-as-usual for human beings (you know: greed, fighting, hate and fear – just enough to recognize this society as human, yet not enough to grind the machine to a halt). Where’d the preachy, preachy come from? Sorry. We’ll save the puzzle of “fixing” society for later…

3. A sadistic maniac not unlike the Saw guy has abducted a group of people and plans to execute them should they fail his logic test.
1. His first social experiment is with 3 people. Once they come to from their gas-induced slumber, a surprisingly nasal and effeminate male voice begins talking from a loudspeaker protruding from the ceiling of their small metallic prison. 
   

2. After the three ex-bullies managed to escape this lunatic unscathed, he rounded up 10 more faces from his past. This time the victims were from his middle school days, where the hurt was deeper and the bullying was more severe. Although he presents them with the same exact test as he presented the 3 before them, he figures that it will be much harder for the 10 to figure out a way of saving their own skin. Surprisingly, 9 of the 10 need not fear death if the group adopts and applies the proper strategy. As before, one of their number will be coin flip away from life or death. What must our 10 abductees do to save at least 9 and hopefully the tenth? They get an hour to writhe around in problem-solving purgatory before their moment of intellectual judgment.

4. Get 16 matches, toothpicks, or something similar. With them, represent the following equation: I + I I + I I I = I I I I

5. Here’s a toughie. You have 12 billiard balls. One of them is known to be a different weight than all of the rest. How can you use a balance scale (of the kind that blind lady on the courthouses holds) to isolate the ball of different weight if you only get 3 opportunities to weigh different quantities of balls. Not only must you find which ball doesn’t have the proper weight, you must also know whether it is too heavy or too light. Get under weigh! (I only promised that problems would not rely on abhorrent puns for their solution; I didn’t promise that I would not make any for their own sake.)

6. You are dreaming. It is dark. You can see nothing. All of a sudden, you hear a click as somebody pulls the chain of a solitary light bulb, faintly illuminating a vast, yet narrow sterile hallway. You seem to be outside of space, observing the hallway while not truly in the hallway at the same time. The nondescript person in nondescript clothing takes a step forward and turns on another light with the same reverberating click. He solemnly continues down the hallway, with each step another click and even more light. For what seems like an eternity this continues until finally you hear foot steps with no more clicking. The hallway is blindingly light as a result of the 1000 clicks you just counted in your head.

Another drone enters the hallway where the first had entered 1000 clicks ago. She walks past the first light bulb and proceeds to the second, whereupon she turns it off with a click. Another two steps and she turns off the 4^th light bulb, and so on as she recedes down the hallway turning every other lightbulb off.

This odd ceremony is far from over, and you are helpless but to observe the strange proceedings. Only after waking can you bring this dream to your analyst who will insist that the compulsive behavior exhibited in this dream is simply your infantile wish fulfillment of presenting the doctor (i.e. the parent) with material for analysis. The analyst knows better than to proceed by treating you as a compulsive neurotic. She informs you that the material of the dream itself acts as a screen to the deeper meaning that your occasional obsessive compulsive behavior of an anal retentive type is actually compensating for your true anal expulsive character. It is from this conflict that the treatment to your neurosis must proceed.

Lucky for you, all that psychobabble is yet to come. You’re still locked in this sterile and boring nightmare. A third person enters the quiet hallway and walks past the first and second light bulbs to pull the chain of third. It goes off. Three more steps and the automaton pulls the 6^th light, turning it on. The cord of every third light bulb is pulled in this fashion, and you silently give thanks that this proceeding wasn’t quite as monotonous as the previous 2.

Before the third person or android has finished its insane task, a fourth enters the hallway. Predictably, it passes the first three light bulbs to pull the cord of the 4^th. Moving faster than its predecessors it moves to the cord of the 8^th, the 12^th and so on. It isn’t long before a fifth android enters your nightmare to pull every 5^th cord.

Android after android enter the hallway, each behaving as you expect them too. The boredom has almost caused you to fall asleep within your dream by the time the 1000^th android pulls the 1000^th cord, turning it off. The silence of the hall without footsteps and clicking overwhelms you, and you wake up. It’s not time to go to work yet, and you reflect on that strange dream. Some lights were left on by the end of that mathematical proceeding, but not many. “How many were left on?” you wonder, “And which ones?” Setting paper to pencil or pencil to paper you resolve to find out.

7. 7 lily pads. 6 frogs. 3 that are dark on the right with 3 on the left that are light. If frogs were to hop only on pads that were empty and allowed to hop over no more than one frog of the other color, how would the light trade places with the dark? They can only move forwards, where for-wards is to-wards the starting position of the frogs of the opposite color.

8. Charles Lutwidge Dodgson, who is more familiar by a name he named himself, was a master puzzle-smith among his many talents. He created a game called doublets, which involves transforming one word into another by the following process: CAT > cot > dot > DOG. Each step must involve the transformation of only one letter, and each step must produce a Scrabble-friendly word in the English language. The previous example was achieved using 2 “links”. 
   

9. There are 2 separate rooms with no windows. You are in a room with 3 light switches. There are no windows, and just a solid door. In the other room (which you cannot see), you know there to be 3 light bulbs. Each of the 3 switches controls exactly one light bulb in the other room, but which one they control is unknown. Your task is to use the switches in such a way as to know the light that each switch controls when you leave the switch room and enter the light room. (no going back and forth; you only get one shot). 
   

10. Sitting in a room with a front and a back, a spider’s positioned and poised to attack. A fly’s on the wall, a foot from the ceiling and opposite the wall from whence the spider will crawl one small foot from the floor. The walls with the creatures, 12 square feet as their features, have between them a floor that is dirty and when counted in feet measures thirty. Despite their positions from ceiling and floor, both bugs sit 6 feet from each wall and no more.