On a plane there is a square, and invisible ink is dotted at a point P. A person with special glasses can see the spot. If we draw a straight line, then the person will answer the question of on which side of the line does P lie $($ if P lies on the line, then he says that P lies on the line $)$.
What is the smallest number of such questions you need to ask to find out if the point P is inside the square?
During the ball every young man danced the waltz with a girl, who was either more beautiful than the one he danced with during the previous dance, or more intelligent, but most of the men $($ at least 80% $)$ – with a girl who was at the same time more beautiful and more intelligent. Could this happen? $($ There was an equal number of boys and girls at the ball.$)$
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 $)$.
In Neverland, there are magic laws of nature, one of which reads: “A magic carpet will fly only when it has a rectangular shape.” Frosty the Snowman had a magic carpet measuring $9 \times 12$. One day, the Grinch crept up and cut off a small rug of size $1 \times 8$ from this carpet. Frosty was very upset and wanted to cut off another $1 \times 4$ piece to make a rectangle of $8 \times 12$, but the Wise Owl suggested that he act differently. Instead he cut the carpet into three parts, of which a square magic carpet with a size of $10 \times 10$ could be sown with magic threads. Can you guess how the Wise Owl restructured the ruined carpet?
What is the maximum number of pieces that a round pancake can be divided into with three straight cuts?
How can you divide a pancake with three straight sections into 4, 5, 6, 7 parts?
Two people had two square cakes. Each person made 2 straight cuts from edge to edge on their cake. After doing this, one person ended up with three pieces, and the other with four. How could this be?