4 criminals are caught and are to be punished. The judge allows them to be freed if they can solve a puzzle. If they do not, they will be hung. They agreed.

The 4 criminals are lined up on some steps (shown in picture). They are all facing in the same direction. A wall separates the fourth man from the other three.

So to summarise :
Man 1 can see Man 2 and Man 3.
Man 2 can see Man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.

The criminals are wearing hats. They are told that there are two white hats and two black hats. The men initially don’t know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.

They are not allowed to turn round or move. They are not allowed to talk to each other. They are not allowed to take their hats off.

Who is the first person to shout out and why?

Bruce is an inmate at a large prison, and like most of the other prisoners, he smokes cigarettes. During his time in the prison, Bruce finds that if he has 3 cigarette butts, he can cram them together and turn them into 1 full cigarette. Whenever he smokes a cigarette, it turns into a cigarette butt.

One day, Bruce is in his cell talking to one of his cellmates, Steve.

“I really want to smoke 5 cigarettes today, but all I have are these 10 cigarette butts,” Bruce tells Steve. “I’m not sure that will be enough.”

“Why don’t you borrow some of Tom’s cigarette butts?” asks Steve, pointing over to a small pile of cigarette butts on the bed of their third cellmate, Tom, who is out for the day on a community service project.

“I can’t,” Bruce says. “Tom always counts exactly how many cigarette butts are in his pile, and he’d probably kill me if he noticed that I had taken any.”

However, after thinking for a while, Bruce figures out a way that he can smoke 5 cigarettes without angering Tom. What is his plan?

“Who shot her?” cried Rogers as he rushed into the hospital three minutes after his ex-wife died from a bullet through her head.

“Just a minute, Mr. Rogers,” said Professor Stiggins. “We’ll have to ask you a few questions-routine, you know. Although divorced for the past six months, you have been living in the same house with your ex-wife, have you not?”

“That’s right,” replied Rogers.

“Had any trouble recently?”

“Well, yesterday, when I told her I was going on a business trip, she threatened to commit suicide. In fact, I grabbed a bottle of iodine from her as she was about to drink it. When I left last evening at seven, however, telling her I was spending the night with friends in Sewickley, she made no objection. Returning to town this afternoon,” continued Rogers, “I called my home and the maid answered.”

“Just what did she say?” inquired Stiggins.

“‘Oh, Mr. Rogers, they took poor mistress to St. Ann’s Hospital abbout half an hour ago. Please hurry to her.’ “She was crying, so I couldn’t get anything else out of her; then I hurried here. Where is she?”

“The nurse will direct you,” said Stiggins with a nod.

“A queer case, this, Professor,” said Inspector Kelley. “These moderns are a little too much for me, I’m afraid. A man and woman living together after being divorced six months!”

“A queer case indeed, Inspector,” mused the professor, “and you’d better detain Mr. Rogers. If he didn’t shoot her himself, I’m confident he knows who did.”

Why did the professor advise the Inspector to detain Rogers?

The emperor’s troops have captured you, the leader, and your 8 soldiers. He says he will execute you all but has given you the chance to take his challenge.

The emperor says that you and your platoon will be free if you survive his challenge, else, you will all die.

The emperor says that he will drug you and your 8 soldiers and put you all in the middle of a dry desert at a crossroads. There are 4 paths – one North, one East, one South, and one West, each which takes 8 hours to walk. One of the paths leads to a village that, if you find, ensures your freedom. When you all wake up, you may lead your soldiers to freedom.

You accept the challenge.

Before the emperor drugs you and your soldiers, he offers his advice. One should not wander off the paths, for if they do, they will surely get lost and die and furthermore you and your soldiers only have a day, 24 hours, to find the correct path to the village. Any more time in the desert and you all will die from thirst and hunger.

When you wake up in the desert you find a note in your pocket from the emperor. It reads: “I forgot to mention – two of your soldiers are my spies. They may or may not lie to you, but it is in their best interest to prevent you from reaching the village. The spies are peaceful, so they will not hurt you or your soldiers.”

As you fold the note up and tuck it away, your soldiers begin to wake up and the challenge begins.

Reaching the village in 24 hours is possible without trickery (digging for water, finding and oasis, having the spies tell you where the village is) and without anyone dying. The emperor has not tried to trick you in anyway either.

You must depend on your logic and reasoning. What is your solution?