The riddle riddle

Anyone who likes logic problems and riddles will have come up with the typical list that has a habit of gutting it, showing that he knows everything even before he has given you time to explain it. If you already know the puzzle, respond quickly before those who may be interested in solving it have had time to try. Even when he is new to him, he manages to show how much he looks like that other he knows and says that it is undoubtedly much more difficult.

This reminds me of that Persian proverb that says "He who does not know, and does not know he does not know, is a fool." Then it is a pleasure to silence him, as in this case I am going to tell you:

Harry is about to teach a geometry problem when he is very rudely interrupted by an insufferable smartie, who says he believes that this is the famous problem known as the old Miter problem, which I popularized myself about fifty years ago and in which a paper has It should be divided into four parts of similar size and shape.

Harry goes on seeing the desire of the clever to ruin the puzzle to everyone and responds: "Very well, then! You have to cut this paper in the smallest possible number of pieces that can fit to form a perfect square. I have forgotten the solution, but here my friend has kindly offered to give it to you, so you can enjoy the fantastic prizes it has for all of you. ”

The problem itself is not as easy as it seems, and it can confuse an expert for a long time until the solution is found. The scholar will be able to realize immediately that the key to the problem is in the beginning of our old friend Pythagoras, who will give us the size of the square.

There are undoubtedly innumerable ways to achieve this feat by cutting the paper into many pieces and thus discover one of these answers. Here lies the merit of the modern school of riddles, which offers many possibilities to ingenuity and skill, since while anyone can find a pretty good answer, a good fan of riddles has the possibility of finding a better one.

* Translation note: The original title of this puzzle is The Smart Alec Puzzle. In the Anglo-Saxon culture, Smart Alec refers to a smart guy, a sabihondo, or a smartie.

Solution

This problem is difficult to solve by experimental methods, but Pythagoras' theorem will be useful. The theorem will give us, at least, the size of the square we will get, since if we divide the paper into four pieces, we will know that 2 and 4 will form a square, while 1 and 3 will form a smaller one. Placing the two squares together, and according to Pythagoras, the line of the hypotenuse that goes from the corner X to the Y at the end of the small square gives us the size of the new square.

If we want to solve the puzzle in the smallest number of pieces, we will first cut sides 1 and 2, and fit them in the center. Then we will cut zigzag stairs, as shown in the figure, and move segment 4 one step down until we get a perfect square. There are many ways to solve the problem with five or even twelve pieces, but the answer we have given you before is both difficult and scientific.