Problems

When Gulliver came to Lilliput, he found that there all things were exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into one of Gulliver’s matchboxes?

Will the entire population of the Earth, all buildings and structures on it, fit into a cube with a side length of 3 kilometres?

Investigating one case, the investigator John Smith discovered that the key witness is the one from the Richardson family who, on that fateful day, came home before the others. The investigation revealed the following facts.

1. The neighbour Maria Ramsden, wanting to borrow some salt from the Richardson’s, rang their doorbell, but no one opened the door. At what time though? Who knows? It was already dark...

2. Jill Richardson came home in the evening and found both children in the kitchen, and her husband was on the sofa – he had a headache.

3. The husband, Anthony Richardson, declared that, when he came home, immediately sat down on the sofa and had a nap. He did not see anyone, nor did he hear anything, and the neighbour definitely did not come – the doorbell would have woken him up.

4. The daughter, Sophie, said that when she returned home, she immediately went to her room, and she does not know anything about her father, however, in the hallway, as always, she stumbled on Dan’s shoes.

5. Dan does not remember when he came home. He also did not see his father, but he did hear how Sophie got angry about his shoes.

“Aha,” thought John Smith. “What is the likelihood that Dan returned home before his father?”.

When Gulliver came to Lilliput, he found that everything was exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into the matchbox of Gulliver?

A cube with a side of 1 m was sawn into cubes with a side of 1 cm and they were in a row (along a straight line). How long was the line?

The volume of a pyramid is \(\frac{1}{3}Bh\), where \(B\) is the area of the base and \(h\) is the perpendicular height. What’s the volume of a regular tetrahedron with side length \(1\)?

The Great Pyramid of Giza is the largest pyramid in Egypt. For the purposes of this problem, assume that it’s a perfect square-based pyramid, with perpendicular height \(140\)m and the square has side length \(230\)m.

What is its volume in cubic metres?

A regular octahedron is a solid with eight faces, all of which are equilateral triangles. It can be formed by placing together two square based pyramids at their bases.

What is the volume of an octahedron with side length \(1\)?