The Lion and the Zebras

The lion plays a deadly game against a group of 100 zebras that takes place in the steppe (an infinite plane). The lion starts in the origin with coordinates (0,0), while the 100 zebras may arbitrarily pick their 100 starting positions. The lion and the group of zebras move alternately:

  • In a lion move, the lion moves from its current position to a position at most 100 meters away.
  • In a zebra move, one of the 100 zebras moves from its current position to a position at most 100 meters away.
  • The lion wins the game as soon as he manages to catch one of the zebras.

Will the lion always win the game after a finite number of moves? Or is there a strategy for the zebras that lets them to survive forever?

Source: Puzzling StackExchange

The zebras can survive forever. They choose 100 parallel strips with width 300m each, then start on points on their mid-lines. If the lion lands on some zebra’s strip, the zebra simply jumps 100m away from the lion, along its mid-line.

Y-Town

In Y-town all crossroads are Y-shaped, and there are no dead-end roads. Is it true that if you start from any point in the city and start walking along the roads, turning alternatingly left and right at each crossroad, eventually you will arrive at the same spot?

Yes, it is true. If you start walking forward, eventually you will end up in a loop. It is easy to see that your entire path, including the starting spot, must belong to this loop. Therefore, eventually you will end up in the starting spot again.

Reverse Puzzling

George is a great puzzler, so I was extremely surprised when he didn’t immediately know the answer to a really famous puzzle. It’s a puzzle that you probably did years ago, and have heard so often you can do it from memory rather than working it out. It’s also not really that difficult, so I was also surprised when it appeared to be stumping him.

“Come on, surely you know this one,” I said.

“I don’t. And don’t call me Shirley.” He answered grumpily. I could tell his mood was declining rapidly, but like any great puzzler he was down and not out, and I watched his facial expression change as he reached into his mental bag of tricks. He nodded towards a conveniently located whiteboard. “Have you got a marker for that?”

I handed him one, and he drew up the following diagram:

He stepped back, admiring his work, beaming proudly. “Well, now the solution is very obvious!” he commented. And indeed it was. The question for you is:

What is the puzzle?

Source: Puzzling StackExchange

The diagram represents the puzzle about the man, trying to cross the river with a fox (F), a chicken (C) and a sack of barley (B). He can carry at most one of them with himself in the boat, and he shouldn’t leave the chicken alone with the fox or with the barley on one side of the river. The red dots represent all admissable configurations and the lines between them all available moves.

Princess in a Palace

A princess is living in a palace which has 17 bedrooms, arranged in a line. There is a door between every two neighboring bedrooms and also a hallway which connects them all. Every night the princess moves through the inner doors from one bedroom to another. Every morning for 30 consecutive days you are allowed to go to the hallway and knock on one of the 17 doors. If the princess is inside, you will marry her. What your strategy would be?

You knock on doors:
2, 3,…, 15, 16, 16, 15,…, 3, 2.
This makes exactly 30 days. If during the first 15 days you don’t find the princess, this means that every time you were knocking on an even door, she was in an odd room, and vice versa. Now it is easy to see that in the next 15 days you can’t miss her.