The standard algorithm of inventive problem solving (ARIZ in Russian and in English) bears a well-known contradiction: it is long/heavy (trying to fit wide range of problems) while it should be light and get-me-at-a-glance one to be attractive and user friendly.

You may find below an algorithm which is free from the contradiction. The algorithm is expressed in a tabular form, which offers not only a clear and straightforward structure but also non-linearity, as it allows the solver to decide which directional path to apply at a certain point in the problem solving process.

The key concepts of TRIZ relative to the proposed methodology are:

**Systemic Thinking**– where is the problem?**Ideality**– what is the way (works as a compass to choose/check the direction)?**Contradictions**– where are the barriers (on the way towards ideality)?**Resources**– where are the solutions (how to overcome the barriers)?

The *key concepts* form the rows of the algorithm table, while the *key stages *form the columns:

The stages, applied progressively throughout the solving process, are:

**Stage 1: Picture**. The problem as a complete picture, with no parts of the picture out of focus. Specifically, the initial problem, with its causes and effects forming a central row of the System Analysis Technique (SAT).**Stage 2: System**. The problem is dissected to find its main systems, their functions, elements, limitations (ineffectively interacting pairs ) and possibilities to eliminate contra-diction of the interactions.**Stage 3: Element**. If the contradiction of interaction is not resolved, we try to eliminate the contradiction of the qualities of separate element(s), choosing the easiest manageable and changeable element(s) of the ineffectively interacting pair(s).**Stage 4: Element in the System**. Do we have an applicable solution? If yes: is the system ready to embrace the modified element(s)? Are the resources involved in the solution the most applicable ones? If not: the problem should be reformulated from the position of the system of a higher level or a different stage of causality.

“The full scale” solution would require going through all the cells, starting from the upper left corner of the table and finishing in the lower right corner with major stages described in the columns. This means that a “normal” solution progresses from top to bottom of a column and then jumps to the upper cell of the next column when reaching the bottom of the previous one (see Figure 2).

However, it can occur that the development of the solution process prompts us to choose a non-traditional track, e.g. making several rounds through the sequence of just one column and then traversing through other cells. In the below example, the solution analysis makes multiple trips through the Picture column then moves along the Resources row to the top of the Element in the System column, bypassing the System and Element stages. Given this capability, I thus refer to the algorithm as a non-linear one: the solver has both the freedom and understanding of what is left behind by making jumps through the problem solving process stages.

Now we are ready to discuss the “horizontal logic” in more details:

**Systemic Thinking**. The logic in this row evolves from “the problem as it is given” to an analysis of main systems / functions / elements / obstacles around the problem. For ‘make-my-system-better’ type problems, the laws for development of technical systems are applied in this row as well.**Ideality**. This entire row implies a “self-resolving” approach: the problems, elements or interactions disappear by themselves, execute a required function or skip/prevent the unwanted function/effect.**Contradictions**. An attempt to make the system/element move to a higher level of ideality often results in contradictions between the interactions within the system or characteristics of its separate elements. The contradiction is to be resolved by inventive principles, analogies etc.**Resources**. The elimination of the contradiction often requires the involvement of resources: energy/force, additional elements, modification of existing elements etc. The analysis of the resources progresses from utilizing hazardous to freely available/inexpensive resources already present within the system and its potential for constructively employing more expensive ones.

A short version of the non-linear algorithm is presented below. The author is ready to present a more detailed description and examples of the algorithm in use later – should there be further interest among the readers.