Problems
Cut the board shown in the figure into four congruent parts so that each of them contains three shaded cells. Where the shaded cells are placed in each part need not be the same.
A family went to the bridge at night. The dad can cross over it in 1 minute, the mom can cross it in 2, the child takes 5 minutes, and grandmother in 10 minutes. They have one flashlight. The bridge can only withstands two people at a time. How can they all cross the bridge in 17 minutes? (If two people pass, then they go at the lower of their speeds.) You can not move along a bridge without a flashlight. You can not shine it from a distance.
Which rectangles with whole sides are there more of: with perimeter of 1996 or with perimeter of 1998? (The rectangles \(a \times b\) and \(b \times a\) are assumed to be the same).
A globe has 17 parallels and 24 meridians. How many parts is the globe’s surface divided into? The meridian is an arc connecting the North Pole with the South Pole. A parallel is a circle parallel to the equator (the equator is also a parallel).
Three hedgehogs divided three pieces of cheese of mass of 5g, 8g and 11g. The fox began to help them. It can cut off and eat 1 gram of cheese from any two pieces at the same time. Can the fox leave the hedgehogs equal pieces of cheese?
Cut the trapezium \(ABCD\) into two parts which you can use to construct a triangle.
On the island of Contrast, both knights and liars live. Knights always tell the truth, liars always lie. Some residents said that the island has an even number of knights, and the rest said that the island has an odd number of liars. Can the number of inhabitants of the island be odd?
Cut the figure (on the boundaries of cells) into three equal parts (the same in shape and size).
In the line of numbers and signs \({}* 1 * 2 * 4 * 8 * 16 * 32 * 64 = 27\) position the signs “\(+\)” or “\(-\)” instead of the signs “\(*\)”, so that the equality becomes true.
The code of lock is a two-digit number. Ben forgot the code, but he remembers that the sum of the digits of this number, combined with their product, is equal to the number itself. Write all possible code options so that Ben could open the lock quickly.