It is known that it is possible to cover the plane with any cube’s net. (You will see it in the film that will be shown at the end of this session). But Robinson, unfortunately, lived on an uninhabited island in the 19th century, and did not know about the film. Try to help him to figure out how to cover the plane with nets \(\#2\), \(\#6\), and \(\#8\) from the previous exercise.
On the first day Robinson Crusoe tied the goat with a piece of rope by putting one peg into the ground. What shape did the goat graze?
On the second day Robinson Crusoe stretched the rope between two pegs, put a ring on the rope, and tied the goat with another rope to the ring. What shape did the goat graze in this case?
On the third day Robinson Crusoe put two pegs again, and decided not to stretch the rope, but to tie the goat with two loose ropes of different lengths to those pegs. What shape did the goat graze on the third day?
One day Robinson Crusoe decided to take his usual walk, and followed his path on a plateau holding his goat on the lead of 1 m length. Draw the shape of the area where the goat could have being eating grass while walking along Robinson Crusoe. The path they followed was exactly in the shape of 1 km\({}\times{}\)3 km rectangle.
Draw how Robinson Crusoe should put pegs and ropes to tie his goat in order for the goat to graze grass in the shape of a semicircle
In his twelfth year on the island Robinson Crusoe managed to tame a wolf, and used him as a guard dog for his goat. He used to tie the wolf with ropes to pegs and other ropes in such a way that there was always a safe place for the goat to escape. Subsequently, he studied the shapes the goat was grazing on the ground.
Draw a picture how Robinson used to tie the goat and the wolf in order for the goat to graze the grass in the shape of a ring
Think of other shapes Robinson’s goat can graze without a wolf, or with a wolf tied nearby. What if Robinson managed to tame several wolves and used them as guard dogs? Can two tied wolves keep an untied goat in a triangle? Can you think of other shapes you can create with Robinson’s goat and wolves?
While studying numbers and its properites, Robinson came across a 3-digit prime number with the last digit being equal to the sum of the first two digits. What was the last digit of that number if among the number did not have any zeros among it’s digits?
Robinson found a chest with books and instruments after the ship wreck. Not all the books were in readable condition, but some of the books he managed to read. One sentence read “72 chickens cost *619* p”. (The starred digits were not readable). He has not tasted a chicken for quite some time, and it was pleasant to imagine a properly cooked chicken in front of him. He also was able to decipher the cost of one chicken. Can you?