You are offered one more formula. It is not so much mathematical as logic and describes our approach to problem solving. We say “our” not because no one else uses it. We do it because the authors of this article noticed it, subjected it to multiple tests, discussed it and use it in their practical work. This approach serves inter alia as a basis of the algorithm of improving problem situations [1].

The employed sequence of actions is simple yet effective. According to it, inventive problem solving procedure can be split into two stages.
The first stage is determining a desired result to be obtained by solving a problem (reducing a temperature, increasing strength, reducing parasitic noise, etc.). N. Khomenko emphasized the importance of this stage in his contradiction-resolving model “Tongs” [2]. It is necessary to determine what exactly should be done for eliminating a problem.
The second stage is searching for and building a system which would facilitate the achievement of the desired result (installing a more powerful cooler, changing the component shape, installing a filter, etc.)
 

The following formula is obtained:

PS = DR + CS,
where:
PS is a problem solution;
DR is a desired result;
CS is a correcting system.

 

It is a general formula. For obtaining an ideal solution, the formula is specified:

IFR = DR + ICS, 
where:
IFR is an ideal final result (a solution obtained without introducing any additional components into an initial system);
DR is a desired result;
ICS is an ideal correcting system.

Thus, to obtain an ideal solution, it is necessary to use an ideal system without losing a required desired result.
An analogy can be drawn with shooting. First, we find a ”target” to be hit, understand what exactly should be improved in a system. Then, without losing the sight of this target, we try to hit the mark at minimum expense.
There is one peculiar feature here which is helpful in problem solving. Quickly finding an ideal system is rather difficult so it is better to use a kind of “adjustment fire method” (Fig. 1). The core of the method is as follows. First, it is necessary to decide how to obtain a desired result in principle, by means of any system without elaborating on its ideality. The system can be complex, expensive or even fantastic – it actually doesn’t matter. It is important that it provide a necessary result. Then, based on the obtained information and better understanding of what kind of system is needed, the process is repeated several times. In so doing, one should be watchful trying: a) not to lose sight of the target (desired result) and b) to make each new system more ideal than the previous one.

 

 
The following chain of solutions is produced:

IPS = DR + IS,
IPS = DR + IS,
IPS (IFR) = DR + IS

 

While solving a problem, system ideality requirements are becoming increasingly stringent and the contradictions are becoming increasingly acute. Accordingly, more and more powerful TRIZ tools are being used for resolving these contradictions.
Generally, this approach better optimizes the mental work expenses than the immediate search for an ideal solution by dealing with two unknowns simultaneously. Determining one unknown abruptly simplifies our equation. 

There are multiple examples of this approach, such as the construction pile problem which is well-known among TRIZ users. Conflicting requirements are imposed on the pile tip. For the pile to easily penetrate the ground while driving, the tip should be sharp and for the pile to support load, the tip should be blunt. 
G.I. Ivanov [3] offered a brilliant way to resolving this contradiction. He proposed providing a pointed pile with an axial opening. After driving the pile to a necessary depth, a small blasting charge is lowered into the channel.  The cavity produced in the ground by explosion is filled with slurry.
When examining the previous solutions to this problem, an interesting picture becomes evident. The sequence of variants of the pile which expands after driving corresponds to our approach (Fig. 2).

 

  
The desired result: a pile should be sharp when driving and blunt after driving. Other inventors also tried to achieve this result: a pile with a withdrawable lobe, a pile with an opening tip and the like. The contradiction was resolved, the desired result was obtained. It was the system for achieving this result that was changing and the degree of its ideality that was growing. Mechanical devices were becoming simpler (screw-type mechanisms were replaced with simple limit stops), the expander design passed to a microlevel (a blast wave and slurry under pressure).  
 

Does the pile design that includes the use of explosive approach the ideal? It depends… The point is that the use of explosive material is regulated by law which can entail certain difficulties. How else can the degree of ideality be improved? The known constructing engineer from Minsk A.V. Shevchenko described the use of a similar method for increasing the pile capacity where explosive material was replaced with water, supplied from above to the nozzles provided in the pile point. Water jets quickly wash out a considerable cavity in the ground. After water has been absorbed by the ground, slurry can be pumped down under pressure into the cavity.

  
Basically, a cavity around the pile point can be formed by a variety of methods and it is not easy to say which of them will prove the most ideal under specific conditions.
 

The authors of this article widely employ the proposed problem-solving method in their work. The examples of solutions to our problems are given in the book [1] on the Target Invention site (http://www.target-invention.com).

 

The analogy between problem solving and shooting is, of course, very conventional. In the course of solving, “shooting” conditions change in a random way and the “target” position is inevitably specified. The ideal system notion itself undergoes changes and corrections at each attempt. Yet each new “shot” brings us closer to the ideal solution and makes the search field narrower. Information about the problem conditions, resources and general problem situation gradually accumulates and a solver gets accustomed to the problem, comes to understand what should be done and what means are more efficient.   

Conclusions: 
1. In inventive problem solving, it is useful to split the process into two stages to be performed preferably separately: а) determining a desired result, b) searching for an ideal system.
2. The search for a system for achieving a desired result should be started from its simplest, “non-ideal” variant and the generation of variants should be repeated until the system ideality satisfies the solver.
3. First, simple contradiction-eliminating methods can be used followed by more complicated and effective ones in the course of solving. 

 

References:

1. Nikolay Shpakovsky, Elena Novitskaya. TRIZ. Practice of Target Invention. Moscow. Forum. 2010.
2. N.N. Khomenko. Effective Education and Problem Management Tools based on OTSM-TRIZ.
http://otsm-triz.com/sites/default/files/ready/jurmala_en.pdf
3. G.I.Ivanov. Formulas of Creative Activity or How to Learn to Invent. Moscow. Prosveschenije. 1994.