Question

"Зачем тебе огниво, служивый ?- удивился мальчик. - Возьми лучше спички". Но солдат не унимался : "Принеси мне огниво , я дам тебе золотой". "Хорошо, - сказал мальчик,- только разрежь мне квадрат 3х3 на две части и квадрат 4х4 на две части так , чтобы из получившихся кусков можно было сложить квадрат". Как это сделать? ( Резать можно только по сторонам маленьких квадратиков)

Answer 1

Надо квадрат 3х3 разрезать на два прямоугольника: 1х3 и 2х3, а от угла квадрата 4х4 отрезать прямоугольник 1х2.
Из полученных частей не составит труда сложить квадрат 5х5.

Answer 2

Problem Analysis

The soldier wants the boy to bring him a flint, but the boy suggests bringing matches instead. The soldier insists on the flint and offers the boy a gold coin in return. However, the boy agrees to bring the flint only if the soldier can cut a 3x3 square and a 4x4 square into two pieces each in such a way that the resulting pieces can be rearranged to form a square. The task is to determine how the soldier can accomplish this, considering that he can only cut along the sides of the small squares.

Solution

To solve this problem, the soldier needs to find a way to cut the 3x3 square and the 4x4 square into two pieces each so that the resulting pieces can be rearranged to form a square.

Let's start with the 3x3 square. Since the soldier can only cut along the sides of the small squares, he needs to find a way to divide the 3x3 square into two pieces that can be rearranged to form a square. One possible solution is to cut the 3x3 square along the middle row, resulting in two pieces: a 3x1 rectangle and a 3x2 rectangle. These two pieces can be rearranged to form a 2x2 square.

Next, let's consider the 4x4 square. Again, the soldier can only cut along the sides of the small squares. One possible solution is to cut the 4x4 square along the middle row and the middle column, resulting in four pieces: two 2x2 squares and two L-shaped pieces. These four pieces can be rearranged to form a 3x3 square.

In summary, the soldier can cut the 3x3 square into a 3x1 rectangle and a 3x2 rectangle, which can be rearranged to form a 2x2 square. He can also cut the 4x4 square into two 2x2 squares and two L-shaped pieces, which can be rearranged to form a 3x3 square.

Conclusion

The soldier can accomplish the task by cutting the 3x3 square into a 3x1 rectangle and a 3x2 rectangle, and cutting the 4x4 square into two 2x2 squares and two L-shaped pieces. These resulting pieces can be rearranged to form a 2x2 square and a 3x3 square, respectively.