Gratte ciel

Gratte ciel or skyline or skyscraper is a type of puzzle where a square grid is given (though rectangular shapes would work as well). Every square in the grid has a skyscraper of 10, 20, 30 or 40 high in a 4×4 grid. The number of different skyscrapers that can be seen from an edge is given along that edge.

For example, if in a row the heights of the skyscraper are 20, 10, 30 and 40 respectively, 3 skyscrapers are visible from the left, as the 10 is hidden behind the 20. Only 1 is visible from the right: the one with a height of 40.

Like many modern puzzles, I don’t know where it was invented first. I have seen it around for several years now.

This one should be a nice and easy introduction:
1) 4×4*

2) 5×5**

3) 5×5**

If you solved it, we have the solution to 1, solution to 2 for you.

For the third puzzle, we have some Hints

Sometimes empty spots are introduced, called parks. they can be regarded as skyscrapers of height 0. It really doesn’t change the puzzle, by simply adding 10 to every height it transforms into the standard form.

Medals

For the Puzzle-Olympics, the International Brain Olympics Committee is purchasing gold, silver and bronze medals. In the medal shop, the bronze, silver and gold medals each have their own prize. Unfortunately for the procurement officer, only sets have price labels.

What is the prize of the fourth set?

If you are puzzled, we have a hint for you.

Inspector S. Mart on the island of KoaLoao

Inspector Simon Mart of Scotland Yard looked at the cabs lined up at the airport. After solving several difficult cases in London, he had been sent to this strange tropical island, KoaLoao. At first sight nothing looked strange. The sky was blue, the leaves of the coconut trees bright green, and the sand was yellow, and the ocean reflected the yellow sunlight as deep blue.

But he knew that the strange thing of this island was the people. The natives of this island fell into two distinct groups: those who always spoke the truth, called TruthTellers, and those who always lied, and were called LieSpeakers.

1) The cabdrivers
He approached the first taxi, and wondered how he could find out if the cab driver was a TruthTeller or a LieSpeaker.
“What’s the cost of a trip to the majestic hotel?” inspector Mart asked.
“Whoah dollar” the taxi driver told him. As the inspector did not understand the local language, the answer was meaningless to him. Then he suddenly realized that even if he had known the language, the answer would have been worthless to him if he didn’t know if the cab driver was a TruthTeller or a LieSpeaker.
He immediately asked: “Are you a TruthTeller?”
The reply came without hesitation:
“Koa, sir!”
Inspector Mart looked around helplessly. The cab driver of the next taxi walked up to him.
“Can you help me, please?” he said to the taxi driver. “Is this taxi driver a TruthTeller?”
The second cab driver answered right away:
“Loao, sir!”
Inspector Marts face cleared up. That taught him something.
He asked a third question, this time to the first taxi driver:
“Would this man” – the inspector pointed at the second cab driver – “call himself a TruthTeller?”
“Loao, sir!” the first taxi driver exclaimed.

Is the First cab driver a TruthTeller or a LieSpeaker?

If you wish you can check your solution.

2) The theft of the Yellow Coconut
Inspector S. Mart looked at the interrogation report of the three suspects of the theft of the Yellow Coconut, a monumental piece of Art by the native artist Art Fruit, symbolizing the fertility of islands in the Paleontic Ocean. Three suspects have been arrested: Art Fruit himself, Bert Friend, and Chuck False. It has already been established that one of them must have stolen the Yellow Coconut from the Royal Museum of Native Art. All three are natives of the island.

Art: I am innocent. Chuck is guilty.
Bert: I am innocent. Chuck is guilty.
Chuck: I am innocent. Art is a LieSpeaker.

Who is guilty?

If you solved it, you can check your solution.