Solving logical problems is an entertaining and rewarding activity. Its peculiarity is that initially there is only a false and true statement, and no formulas. Let's consider several basic methods of solution, which have their own area of effectiveness.
Instructions
Step 1
The method of reasoning - the most straightforward - is based on sequential reasoning (arising from the condition of the problem), and their verification for truth or falsity, and all subsequent statements are based on the verified original.
For example. The age of the mother and daughter is 98 years in total. The daughter was born when my mother was 22 years old. How old are both? Solution: since the difference in their age is 22 years (it was at this age that the mother had a daughter), then 98 - 22 = 76 (years). This is twice the age of the daughter, then 76: 2 = 38 (years). This means that mothers are 98 - 38 = 60 (years).
Step 2
The method of tables is a visual method that implies building a table according to the conditions of word problems and sequentially filling it with the numbers 0 or 1, depending on the conclusions obtained (false-true).
For example. There is an 8 liter vessel full of water.
How to pour out 4 liters if there are empty containers with a volume of 3 and 5 liters? Decision:
Step 3
The method of block diagrams is applicable to solving problems about containers and weights and is much more convenient than the method of enumerating options (which does not allow us to derive general rules). First, commands are formed (identical to the operations performed), and then their schematic sequence is built. This is the well-known flowchart in programming that leads to the solution of the problem. The logical continuation of this method is the computer-assisted solution method. The essence of which, in the transfer of the obtained algorithm to the programming language.
Step 4
The algebraic solution method involves solving systems of logical equations. All statements arising from the condition of the problem are assigned letter designations and written in the form of formulas. Solving the system of the obtained equations (multiplying one by the other), the true statement is deduced.
Step 5
A graphical way of solving the system is also possible. For this, a diagram of logical relationships ("logical conditions tree") is drawn based on the obtained equations of the system. Moreover, a logical sum implies branching, and a product means the following conditions one after another. The decision comes from analysis. This also includes the Euler circles method - the construction of a geometric scheme that reflects the intersection or union of sets.
Step 6
No less interesting is the billiard method based on the theory of trajectories.
However, for its detailed consideration, a separate, very entertaining, article will be required.
