The police were investigating a string of burglaries where only gold and silver rings were stolen. Their main suspect, Egon Herzlich, worked at a shop and collected small metal pyramids. During a search of his home, the police found Herzlich's collection of over 20 pyramids of different sizes, along with detailed records of each pyramid's dimensions. Inspector Knick had a genius idea while watching melted margarine that he believed could provide additional evidence to arrest the thief.

1. Fried eggs
It was jinxed. The third burglary in a row and the police hadn’t had any success in finding the thief. Not any success? That was not comlpetely right. Actually they had a suspect, but without any proof, they couldn‘t arrest him.
Let‘s start with the burglaries. They were very ordinary burglaries at night. Everything happened calmly, without violence, when the owners were sleeping peacefully in their beds. Only one thing had been stolen everytime: rings of gold and silver. No computers or similar objects, just rings. Often the burglaries were noticed only days later, because the burglar changed nothing in the house. The last burglary in this vein happened at the house of the Geron family. Mister and Mrs. Geron were married and Mrs. Geron wore her wedding ring even at night. However Mister Geron took it off every evening. The metal was two mm thick and 4 mm wide. The couple knew the exact data, because the ring had been a custom-made product, because of the reason that Mister Gerons fingers were very small for a man. The rings inner diameter was 2 cm, it looks plain, but very elagant too. However, it was unfortunately lost now.
The suspect, a shop assistent named Egon Herzlich, didn’t have an alibi for any oft he burglaries, but that wasn‘t enough evidence for the prosecutor. The only suspecous thing was his behaviour at work. One day his chief, Mister Turm, called the inspector Mister Knick, to inform him about his colleague, because of the scores of affliction. He was being very indescriet and kept asking people about their family status. He was especially interessted in married customers and asked them about their wedding rings. In a conversation with Mister Turm, Mister Herzlich had denied everything and Mister Turm left it at that. After that the police conducted a house search at Mister Herzlichs, but there wasn’t anything conspicuous at all: an unbelievable amount of shoes, as he explained, sample copies given by his boss, a knife-block with ten very sharp knifes, but in this case nobody was knifed, and an impressive collection of small silver and gold quadratic pyramids in different sizes. But no pyramids has been stolen, just rings. „Nice collection!“ said Commissar Knick. „ Yeah!“ answered Egon Herzlich, „I’ve got more than 20 pyramids already. I indexed all oft hem!“ He held nspector Knick a list right in front of his face. „I want to create a chess game with them.“ „And how will you distinguish which pyriamide is which chessman?“ inspector Knick asked very interessed. „That’s very easy. You see it because of the dimensions. The chessmen have got- it just sais it here.“ He showed inspector Knick the list again:

2. Edge length of the quadratic base
Hight of the pyramid
Amount of the finished golden chessmen
Amount of the finished siver chessmen
Knight
1,5 cm
1,7 cm
1
0
Bishop
1,3 cm
2,2 cm
0
1
Queen
1,5 cm
2,5cm
2
0
King
2 cm
2,5 cm
1
0
Rook
1,3 cm
1 cm
1
0
Pawn
1 cm
1 cm
0
3
„The chessmen have got differently sized bases and heights. The measurements aren’t exact, but that doesn’t matter. The important measurements are right. The queen and the king for example are the biggest ones. The queen has a smaller base than the king. The pawns have got the smallest base and height. As you see many of the chessmen are still missing, my collection isn’t complete yet. I’ve got a lot of work.“ He started dreaming. Inspector Knick regarded the list politely, but catched hisselve when he started dreaming as well, namely about his closing-time. To play some chess, that would be nice. In the evening inspector Knick returned home very depressed, as so often: The investigation isn’t proceed. Because that, the dinner was just fried eggs and a piece of bred. While he was watching how the margarine melt and changed it’s shape, a genious idea stroke him, how he could arrest the thief with additional evidence…

3. 1. A genious idea stroke inspector Knick, while he was watching how the margarine melt. What could he has been thinking about?
Answer:
2. What happened to the wedding ring of Mister Geron? Prove your idea with a detailed calculation.
Answer:
3. How wide would the ring have had been, if it had been turned into a king?
Answer:

4. 4. What would have been the height of the king if it had been made out of the wedding ring?
Answer:
5. Write down other figures you can convert the ring into. (exact dimensions)
6. Write down instructions, how to produce the chessmen and describe, how to calculate the dimensions of a pyramide.