# Puzzle 3 – Inductive Reasoning

The previous two puzzles were based on **deductive** reasoning. where the conclusions are certain given the information you are given. These puzzles involve **inductive** reasoning, where the reasoning process is probable but not certain.

Inductive reasoning tests are popular screening assessments used by employers as part of the assessment process. They provide valuable information on the way you think and react to new rules and situations. They are also used for culture-fair IQ tests. In these types of tests, inductive reasoning requires identify a pattern or consistency among sets of objects and predict what is the next expected object in the sequence.

In this problem you need to dimensionalize the object attributes into line orientation, dots, and shapes.

In the first row the line orientation is horizontal; in the second row it is vertical. The first two shapes in the third row are diagonal, and we can infer that the missing shape will have a diagonal line too.

Each row has a circle, vertical oval, and horizontal oval. So we can infer that the missing shape will have a vertical oval.

Each row has outer dots, a central dot and no dots, so we can infer that the missing shape will have outer dots.

The only shape fulfilling these criteria is G.

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This matrix problem involves simple maths operations.

If you superimpose the first and second figure of each row, and subtract any element that is shared between them, you are left with the third figure in the row. Take the first row. The shared element here is the left line. Take the second row. The shared element here is the bottom line and the bottom left to top right diagonal line. In the bottom row, the shared element is the diagonal line, leaving a square with a dot (there is always a dot in each figure) – i.e. answer D.

**Mindware strategies for Raven’s matrices tests**

The most famous type of matrices IQ test is the Raven Advanced Matrices Test.

Each Ravens test has the same format: a 3 x 3 matrix in which the bottom right entry is missing, and must be selected from 8 alternatives.

Solving Raven’s matrices type problems essentially requires figuring out the underlying ** rules** that explain the progression of shapes.

Here is an example to try to figure out:

The correct answer is 5. The variations of the entries in the rows and columns of this problem can be explained by 3 rules.

1. Each row contains 3 shapes (triangle, square, diamond).

2. Each row has 3 bars (black, striped, clear).

3. The orientation of each bar is the same within a row, but varies from row to row (vertical, horizontal, diagonal).

From these 3 rules, the answer can be inferred (5).

**5 Rules For Matrices Problem Solving (Advanced Matrices Test)**

John Raven designed all the problems for his Advanced Matrices test to be based on five basic types of rule. Each problem might have combinations of different rules or different instances of the same rule.

In order to solve Advanced Raven Matrices Test problems effectively, you will benefit from learning these rules,

These are the rules:

1. **Constant in a row. **This is ‘rule 3’ in the matrix example above – the orientation of the bar is the same in each row, but changes down a column.

2. **Quantitative progression. **An increase or decrease between adjacent entries in size, position or number. An example of this rule is shown below:

The correct answer is 3. The number of black squares in each entry increases in the top row from 1 to 2 to 3. Similarly, the number of black squares in the first column decreases from 3 to 2 to 1.

3. **Figure addition or subtraction.** A figure from one column is added to or subtracted from another column to produce the third. An example is given below:

Correct answer 8

4. **Distribution of 3 values. ** Three values of a category such as shape are always present in each row. Two examples of this rule are shown in the first matrix we looked at above. Each row contains 3 shapes (triangle, square, diamond), and each row has 3 bars (black, striped, clear).

5. **Distribution of 2 values. ** Two values of a category such as shape are always present in each row, but the third is null/irrelevant. An example of this is given below.

The correct answer is 5. Each figure element (horizontal line, vertical line, V shape) occurs two times in each row.

## Finding corresponding elements

In problems with more than one rule, the problem solver must figure out which elements in the puzzle are governed by the same rule – something that can be called ‘correspondence finding’.

An example of a correspondence problem is shown below:

The correct answer is 5. Figuring out what corresponds to what requires that you form ** hypotheses** in your mind and test them out. A hypothesis is an imagined explanation or prediction that needs to be tested.

In the example above, one hypothesis is that one rule applies to the bars, another rule applies to the dark curves, and another rule applies to the straight lines. Although it’s true that each row has two of each type of shape, this hypothesis doesn’t explain the number or orientations of the different elements. Another hypothesis is needed. In the end it is orientation (vertical or horizontal) that is the basis of the rules needed to solve this problem. In each row there are always 1, 2 and 3 horizontal elements and 1,2 and 3 vertical elements. In addition to this, 1,2 and 3 elements of each shape are distributed across the three rows.

**Additional training resources**

For matrices tests (e.g. Raven’s Advanced Progressive Matrices), you can train with this forum resource here. Or additional strategies here.

This is a good resource for job tests.

The Raven’s (standard) Progressive Matrices Test – the original can be taken here. The fee is 20 Euros. This is a valid IQ test, and relative to other professionally administered IQ tests not costly. This is not the Advanced Progressive Matrices test.

Alternative Matrices tests based on Raven’s test and using similar principles can be found here (Italian text). To get your results after taking either test, you need to enter your age in the box provided and then click on ‘IQ’.

Smart-kit.com Matrices Test puzzles. Many to try out here.

SimilarMinds Matrices Test – scored.