Snow White cut out a big square of cotton fabric and placed it in a chest. The first gnome came, took out the square of fabric from the chest, cut it into four squares, put these back in the chest and left. Later the second gnome came and took out one of the squares and then cut it into four pieces and placed all of these in the chest. Then came the third gnome. He also took out one of the squares and cut it into four squares and put them all back in the chest. The rest of the gnomes also did the same thing. How many squares of fabric were in the chest after the seventh gnome left?
Carpenters were sawing some logs. They made 10 cuts and this produced 16 pieces of wood. How many logs did they saw?
The tower clock chimes three times in 12 seconds. How long will six chimes last?
This problem is from Ancient Rome.
$\\$ A rich senator died, leaving his wife pregnant. After the senator’s death it was found out that he left a property of 210 talents (an Ancient Roman currency) in his will as follows: “In the case of the birth of a son, give the boy two thirds of my property (i.e. 140 talents) and the other third (i.e. 70 talents) to the mother. In the case of the birth of a daughter, give the girl one third of my property (i.e. 70 talents) and the other two thirds (i.e. 140 talents) to the mother.”
$\\$ The senator’s widow gave birth to twins: one boy and one girl. This possibility was not foreseen by the late senator. How can the property be divided between three inheritors so that it is as close as possible to the instructions of the will?
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?
Ten people wanted to found a club. To do this, they need to collect a certain amount of entrance fees. If the organizers were five people more, then each of them would have to pay £100 less. How much money did each one pay?
It is known that in January there are four Fridays and four Mondays. What day of the week is January 1st?
In a room, there are 85 red and blue balloons. It is known that: 1) at least one of the balloons is red; 2) from each arbitrarily chosen pair of balloons at least one blue. How many red balloons are there in the room?
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?
The old shoemaker Carl sewed some boots and sent his son Hans to the market to sell them for £25. Two disabled people came to the boy’s market stall $($one without a left leg, the other without a right one$)$ and was asked to sell each of them a boot. Hans agreed and sold each boot for £12.50.
When the boy came home and told the whole story to his father, Carl decided that his son should have sold the boots to the disabled buyers for less – each for £10. He gave Hans £5 and ordered him to return £2.50 to each disabled buyer.
While the boy was looking for the disabled people at the market, he saw that someone was selling sweets and as could not resist, spent £3 on sweets. After that, he found the disabled buyers and gave them the remaining money – each got £1. Returning home, Hans realised how badly he had acted. He told his father and asked for forgiveness. The shoemaker was very angry and punished his son by sending him to his room.
Sitting in his room, Hans thought about the day’s events. It turned out that since he returned £1 to each buyer, they paid £11.50 for each boot: 12.50 – 1 = 11.50. So, the boots cost £23: $2 \times 11.50$ = 23. And Hans spent £3 on sweets, therefore, it total, there were £26: 23 + 3 = 26. But there were only £25! Where did the extra pound come from?
Fred and George together with their mother were decorating the Christmas tree. So that they would not fight, their mother gave each brother the same number of decorations and branches. Fred tried to hang one decoration on each branch, but he needed one more branch for his last decoration. George tried to hang two toys on each branch, but one branch was empty. What do you think, how many branches and how many decorations did the mother give to her sons?
The grandad is twice as strong as the grandma, the grandma is three times stronger than the granddaughter, the granddaughter is four times stronger than the dog, the dog is five times stronger than the cat and the cat is six times stronger than the mouse. The grandad, the grandma, the granddaughter, the dog and the cat together with the mouse can pull out the pumpkin from the ground, which they cannot do without the mouse. How many mice should be summoned so that they can pull out the pumpkin themselves?
In a basket, there are 30 red and green apples. Among any 12 apples there is at least one red one, and among any 20 apples there is at least one green one. How many red apples and how many green apples are there in the basket?
The natural number a was increased by 1, and its square increased by 1001. What is a?
10 people collected a total of 46 mushrooms in a forest. It is known that no two people collected the same number of mushrooms. How many mushrooms did each person collect?
In a room there are some chairs with 4 legs and some stools with 3 legs. When each chair and stool has one person sitting on it, then in the room there are a total of 39 legs. How many chairs and stools are there in the room?
The intelligence agency of the Galactic Empire intercepted the following coded message from the enemy planet Medusa: $ABCDE+BADC=ACDED$.
It is known that different numbers are represented by different letters, and that the same numbers are represented by the same letters. Two robots attempted to decode this message and each one got a different answer. Is this possible, or should one of the robots be melted down as scrap metal?
The numbers in an equation were replaced with letters (the same numbers were replaced with the same letters and different numbers with different letters). The result was: $ABCDE+AFCD=GHDJD$. Find the number which is represented by $GHDJD$.
A rectangle of size $199\times991$ is drawn on squared paper. How many squares intersect the diagonal of the rectangle?
In January of a certain year there were four Fridays and four Mondays. Which day of the week was the 20th of January in that year?
First suppose that the 1st of January is a Monday that year. This can’t be true since then this January would have 5 Mondays as shown in the image below, so we have a contradiction. Similarly, we can see below that if January started on any day of the week apart from Tuesday then there would either be five Mondays or five Fridays in this month. Therefore this January must start on Tuesday. Then it is simple to see that the 20th of January is a Sunday.
Sunday.
