# Varia

I

In one pen, tells an old Chinese task, there were rabbits and chickens. It was together 35 heads and 94 legs. How many chickens were there, and how many rabbits?

This problem is solved very easily with the help of algebra.

II

Alcuin, mentioned above, is the author of such a task:

The greyhound chases the hare, who is in front of him, Fr. 150 Stop. The hare's jump is 7 Stop, and the greyhound jump at the same time 9 Stop.

After how many jumps the hare will catch up?

III

An old legend has it, that the Bohemian princess Libusha had promised to give up her hand of the three knights who were competing for her, which will first solve the problem of the following content:

How many plums are in the basket, of which he will give half of the entire contents and one plum to the first, the other half of the rest and one plum, and finally the third half of the rest and three plums, after which the basket will be empty.

IV

The peasant woman brought eggs to the market. She sold half of the total amount and one egg to the first buyer, the other half of the rest and one egg, the third - again half of the remaining eggs and one egg. Then it was left in her hair 10 eggs. How many eggs did she have originally?

V

Nine children divided the apples they owned. The first one took one apple and the rest, the second 2 apples

i y reszty, third 3 apples and ^ rest and so on. It turned out then, that they all got an equal number of apples. After how much, namely?

WE

It was in the 19th century. One gentleman was asked, when he was born.

— Miałem pełnych lat x w roku x².

This citizen was born in 1806.

1806 + 43 = 43²

There would be such a solution in the twentieth century:

1892 + 44 = 44²

But how to get there?

VII

And that was still before, when neither the cars were known, no railroad, when even kings rode "spaced."” horses.

A postmaster was asked then, how many horses the king ordered for a change of harness. The postmaster replied: “Half of the horses ordered are ridden by the king himself, half of the rest is his minister, half of the remaining horses and the servants ride half a horse, and the other horses are ridden by the money ".

How many horses were ordered?

VIII

The pond is overgrown with duckweed. Every two days, the area covered with duckweed doubles. The entire pond was overgrown in the course 64 days. After how many days a quarter of a pond was overgrown with duckweed?