How to learn to solve problems?
Each task has its own characteristics, eachdecision individually. But the approach to finding solutions has much in common for most tasks. For example, the problems in chemistry are written in the article How to solve problems in chemistry, and about problems in genetics - in How to solve problems in genetics. We will tell you how to learn to solve logical and mathematical problems.
How to solve logical problems
Most logical tasks can be solved using tables. Usually enough one table, if the data is too much, you have to make two tables.
Solution Algorithm
First, you need to carefully read the problem, determine the number of the same variables and draw the corresponding table. For example, such a task:
Three fans of the "Formula-1" argued about the upcoming race. "You'll see, Schumacher does not come first," John said. "The first will be Hill."
"No, the winner will be Schumacher," Nick objected. "And Alesi will not be the first."
Peter did not agree: "Hill does not see the first place, but Alesi pilots the most powerful car."
According to the results of the race, it turned out that each of the two assumptions of the two friends was confirmed, and both assumptions of the third of the friends were wrong. Who won the stage of the race?
In this problem we have two groups of variables: three friends and their opinions. So, we can draw a table in which you can write the names of the riders horizontally - possible winners, and vertically the names of friends. Their views will fit into the appropriate cells: we'll put the pluses where the rider is considered the winner, the minuses - where the rider is denied a win.
|
|
Schumacher |
Hill |
Alesi |
|
John |
-- |
+ |
|
|
Nick |
+ |
|
- |
|
Peter |
|
- |
|
Suppose that John is right, and Hill won. But then both Nick and Peter are wrong, which contradicts the conditions of the problem. So, John was mistaken, but two other fans are right. Then there is no contradiction.
The table in such problems is necessary for clarity. When you look at it, you can immediately cover the whole array of data. This is especially important when the data is larger and difficult to keep in mind.
How to solve mathematical problems
As in any task, you must carefully readconditions and record them briefly and clearly, ruthlessly throwing out all the lyrics. For example, such a task: "During the heavy rain at the bus stop, there were 12 people. I drove up the bus and sprinkled mud on the five. The rest managed to jump into the thorn bushes. How many scratched passengers will go on the bus, if it is known that three of them could not get out of the thorn bushes? ".
Do not worry about the passengers, although it's cruel. Let's concentrate on the numbers. So:
- total - 12 people;
- 5 spattered, but without scratches;
- 3 stuck in the bushes.
This simple problem for the second class is solvedeasily. For more complex tasks, you may need to know the formulas, as in the article How to solve traffic problems. First you need to write out in the draft all the formulas that can be useful in this case.
Now we need some value, most often the one we need to find, take for X and, using the formulas and conditions of the problem, write down how all quantities are related.
In the above task for X we take the number of scratched passengers on the bus. X is less for 3 of those who hid in the bushes, and there hid 12 - 5 sprayed. Hence, X = 12 - 5 - 3 = 4.
