Jack the goldminer extracted 9kg of golden sand. Will he be able to measure 2kg of sand in three goes with the help of scales: a) with two weights of 200g and 50g; b) with one weight of 200g?
One day a strange notebook was found on the stairs. It contained one hundred statements:
“There is exactly one incorrect statement in this notebook”;
“There are exactly two incorrect statements in this notebook”;
“There are exactly three incorrect statements in this notebook”;
“There are exactly one hundred incorrect statements in this notebook.”
Are any of these statements true, and if so, which ones?
In a room, there are three-legged stools and four-legged chairs. When people sat down on all of these seats, there were 39 legs $($human and stool/chair legs$)$ in the room. How many stools are there in the room?
Using five nines, arithmetic operations and exponentiation, form the numbers from 1 to 13.
Using five eights, arithmetic operations and exponentiation, form the numbers from 1 to 20.
Using five sevens, arithmetic operations and exponentiation, form the numbers from 1 to 22.
Using five sixes, arithmetic operations and exponentiation, form the numbers from 1 to 14.
Using five fives, arithmetic operations and exponentiation, form the numbers from 1 to 17.
Using five fours, arithmetic operations and exponentiation, form the numbers from 1 to 22.
Using five threes, arithmetic operations and exponentiation, form the numbers from 1 to 39.
Using five twos, arithmetic operations and exponentiation, form the numbers from 1 to 26.
Six sacks of gold coins were found on a sunken ship of the fourteenth century. In the first four bags, there were 60, 30, 20 and 15 gold coins. When the coins were counted in the remaining two bags, someone noticed that the number of coins in the bags has a certain sequence. Having taken this into consideration, could you say how many coins are in the fifth and sixth bags?
Fill the free cells of the “hexagon” $($see the figure$)$ with integers from 1 to 19 so that in all vertical and diagonal rows the sum of the numbers, in the same row, is the same.
Four friends came to an ice-rink, each with her brother. They broke up into pairs and started skating. It turned out that in each pair the “gentleman” was taller than the “lady” and no one is skating with his sister. The tallest boy in the group was Sam Smith, Peter Potter, then Luisa Potter, Joe Simpson, Laura Simpson, Dan Caldwell, Jane Caldwell and Hannah Smith. Determine who skated with whom.
On the table four figures lie in a row: a triangle, a circle, a rectangle and a rhombus. They are painted in different colors: red, blue, yellow, green. It is known that the red figure lies between the blue and green figures; to the right of the yellow figure lies the rhombus; the circle lies to the right of both the triangle and the rhombus; the triangle does not lie on the edge; the blue and yellow figures are not next to each other. Determine in which order the figures lie and what colors they are.
Decipher the following rebus $\\$
All the digits indicated by the letter “E” are even $($ not necessarily equal $)$; all the numbers indicated by the letter O are odd $($ also not necessarily equal $)$.
There are 6 locked suitcases and 6 keys for them. It is not known which keys are for which suitcase. What is the smallest number of attempts do you need in order to open all the suitcases? How many attempts would you need if there are 10 suitcases and keys instead of 6?
The stepmother, leaving for the ball, gave Cinderella a sack which contained a mixture of poppy and millet, and ordered them to be sorted. When Cinderella was leaving for the ball, she left three sacks: one contained millet, the other contained poppy, and in the third – a mixture that had not yet been sorted. In order not to confuse the sacks, Cinderella attached a label to each of them that said: “Poppy seed”, “Millet” and “Mixture”. The stepmother returned from the ball first and deliberately swapped all of the labels in such a way that on each sack there was an incorrect inscription. The fairy godmother managed to warn Cinderella that now none of the labels on the sacks were correct. Then Cinderella took out only one single grain from one sack and, looking at it, immediately guessed what was in each sack. How did she do this?
Do you think that among the four consecutive natural numbers there will be at least one that is divisible a) by 2? b) by 3? c) by 4? d) by 5?
In Wonderland, an investigation was conducted into the case of a stolen soup. At the trial, the White Rabbit said that the soup was stolen by the Mad Hatter. The Cheshire Cat and the Mad Hatter also testified, but what they said, no one remembered, and the record was washed away by Alice’s tears. During the court session, it became clear that only one of the defendants had stolen the soup and that only he had given a truthful testimony. So, who stole the soup?