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?
Prove the divisibility rule for \(3\): the number is divisible by \(3\) if and only if the sum of its digits is divisible by \(3\).
Sophia is playing the following game: she chooses a whole number, and then she writes down the product of all the numbers from \(1\) up to the number she chose. For example, if she chooses \(5\), then she writes down \(1\times 2 \times 3 \times 4 \times 5\). What is the smallest number she can choose for her game, such that the result she gets in the end is divisible by \(2024\)?
While studying numbers and their properties, Robinson came across a three-digit prime number whose last digit equals the sum of the first two digits. What are the options for the last digit of this number, given that none of its digits is zero?
Prove the divisibility rule for \(4\): a number is divisible by \(4\) if and only if the number made by the
last two digits of the original number is divisible by \(4\);
Can you come up with a divisibility rule for \(8\)?