Logic Puzzles are a Powerful Way to Train Your Brain

Inside: Logic puzzles are a powerful way to train your brain to sharpen your inductive and deductive reasoning skills.  If you are a student of science, both of these skills are vital in research and working with the scientific method.  Both of these reasoning skills are also used daily navigating life and all of the potential choices of action required.

Logic puzzles are a great way to practice your reasoning skills.  We use various forms of logic every day.  There are 3 types of logical reasoning:

1. inductive
2. deductive
3. abductive

The main difference between inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory.  Inductive reasoning moves from specific observations to broad generalizations, and deductive reasoning the other way around.

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The scientific method uses both deductive and inductive reasoning. Scientists use inductive reasoning to form hypotheses and theories. They use deductive reasoning to apply the theories to specific situations. So it is very important for kids to develop these two types of reasoning.

Sudoku puzzles and grid logic problems are a forms of deductive reasoning. I love both of these types of puzzle and do them regularly.

Pattern puzzles are inductive reasoning. You have to figure out the rule or rules that link the elements of the puzzle together. Kids begin inductive reasoning very early on in math programs by getting a list of numbers or letters and figuring out what comes next.

Inductive Reasoning

Inductive reasoning begins with specific observations and moves to broad generalizations.  It is used daily and also in science as part of the scientific method.  Let’s look at the following example:

• Everyday I see my neighbor’s dog it barks at me.
• At the shelter, all of the dogs bark at me.
• Therefore, I make the conclusion that all dogs hate me.

So, I see a pattern.  Dogs bark at me in in at least two circumstances.  So I make a broad conclusion that fits my observations, that all dogs hate me.  As I meet more dogs and see their reactions to me, I might revise that conclusion.

All forms of inductive reasoning fit the form of taking specific observations and coming up with a broad conclusion that is likely to fit them.

There are 5 types of inductive reasoning:

1. inductive generalizations
   • using a small sample, you make generalizations about a whole population
     • all of my dogs bark at cars; therefore, all dogs bark at cars
2. statistical induction
   • using a small set of statistics to make a generalization about a whole population
     • 95% of the dogs in my neighborhood bark at cars, so 95% of all dogs bark at cars
3. causal inference
   • using inductive logic to create a link between your hypothesis and your observations
     • in the fall, there are Canada Geese on my fields so every fall I will see geese on my fields
4. analogical deduction
   • creating a hypothesis by analyzing 2 or more similar observations
     • Tuck and Rosco are both guard dogs and both bark at cars
     • Dakota is also a guard dog so he will bark at cars
5. Predictive Induction
   • making a future conclusion based on past information
     • in the past, Canada Geese have always come to our field in the fall; therefore, this fall, Canada Geese will come to our fields

Deductive Reasoning

Deductive reasoning begins with a general idea and makes a specific conclusion from it.  For deductive reasoning to work, your general ideas must be true.  For example,

• Leaves of deciduous trees fall off in autumn.  Maple leaves fall off in autumn.  Thus, Maple trees are deciduous.

Deductive reasoning can sometimes backfire however.  Take this example,

• All swans are white.  Jessica is white.  Therefore, Jessica is a swan.

It is easy to make overgeneralizations from some observations.  When making deductions, it is helpful to make sure your conclusion makes sense.

Sudoku puzzles use deductive reasoning.
Tim Stellmach, CC0, via Wikimedia Commons

Abductive Reasoning

This type of reasoning is used a lot.  You are using incomplete observations and coming up with the likeliest explanation.  It is used by doctors all the time.  Patients explain their symptoms.  Doctors then are relying on perhaps partial symptoms to come up with a diagnosis.  A patient may fail to report all of their symptoms.  If they are evaluating an unconscious patient, all symptoms may not be apparent from direct observation.  In either case, the doctor must make the best prediction they can based on incomplete observations.  Often the best prediction is true in abductive reasoning but often it is a starting point.  More observations will often lead to a new and/or better prediction.

Abductive reasoning lead to out of the box thinking.  It can lead to leaps of logic that lead to revolutionary ideas.  Einstein used abductive reasoning to develop his theory on space-time which has stood the test of time.

Drfederico, CC BY-SA 4.0, via Wiki Commons

Logic Puzzles and Reasoning

Many logic puzzles use deductive reasoning.  Suduku uses deductive reasoning.  There are specific rules for this game:  numbers from 1 to 9 are used.  They are used once in each row and each column as well as once in each subsection of the grid.  The player figures out where to place numbers based on the rules of the game and the numbers already placed in the grid.

Grid logic puzzles also use deductive reasoning.  The player is given a bunch of clues.  From these clues, they need to figure out the relationships between different people, places and things.

Pattern problems commonly used in primary math are great examples of inductive reasoning.  Here you need to figure out the pattern first and then fill in the next few numbers or symbols based on the pattern rule.

2, 5, 11, 23, 47,  ___, ___, ___