The task of developing and training analytical thinking

To make a successful career in commerce, management and the IT industry, it is important to have an analytical mindset. But can it be developed? And what about those who, as they say, have the logic of “you”? The fascinating logical problems for mathematicians and humanists that we collected in our article will help.



Phere Logical Problems for Mathematicians

1. Math and time
   There is a clock on the wall that shows 3 hours and 15 minutes. Can you figure out how many degrees between their arrows?
   
   
   
2. Chess and dominoes
   Imagine a chessboard. It has 64 cells that can be closed with 32 domino chips. Now imagine that two extreme black cells at the ends of the board were removed. Is it possible to close the board 31 with dominoes?
   
   
   

Answers.

1. Math and time
   The first impulse is to say "0." After all, visually imagine that the minute hand should be over the clock. But if you think about it, it becomes clear that there must be an angle. After 15 minutes, the hour hand should shift slightly in the direction of the number 4. It remains to count how many degrees.
   
   
   
   Well, let's get started! As project managers are taught, any complex problem must be broken down into components. But the clock, perhaps, still will not disassemble. Instead, determine how many degrees the short hand shifts in an hour, and then in a quarter of an hour. The whole dial is 360 degrees. So in an hour, the hour hand shifts by 360 / 12 = 30 degrees. Then for 15 minutes it will be 30/60 x 15 = 7.5 degrees. Answer: at 3 hours 15 minutes, the angle between the hands is 7.5 degrees..
   
   
2. Chess and dominoes
   As with many other complex problems, the problem here is to formalize the condition. “Maybe, maybe not. You have to try, the average student will say. We will try to look at the condition from a different angle. To do this, you need to try to find a suitable analogue of the task. Not necessarily from the same category.
   
   Peels
   
   Each domino chip covers two adjacent cells. What color are they? Naturally different, since the monochrome cells on the chessboard are located diagonally. What does that give us? The path to a solution, though it won’t be too obvious.
   
   729490
   
   
   
   Let's try to formulate a similar, but more understandable task. For example, in one village there were 32 bachelors and 32 unmarried girls. The matchmaker was able to make 32 pairs of them. Unfortunately, at the last minute, two guys were drafted into the army. Will the remaining men and women make up 31 pairs? Clearly not. Indeed, there are only 30 grooms and 32 brides. So, no matter what, and two ladies, if they are traditional orientation, will be out of business. Similarly, a board without two single-colored cells is not It is impossible to close 31 dominoes..
   
   

These are some interesting logical problems. The answer to them will not be calculated, much less remembered. After all, to solve it, you need to think creatively and analytically. And this helps us to successfully find a way out of the most difficult life situations.