THOG problem facts for kids

The THOG problem is a special kind of logic puzzle created by a smart thinker named Peter Wason. He designed it to show how our brains sometimes struggle with tricky problems.

The four symbols used in the THOG problem.

What is the THOG Problem?

Imagine you see four different symbols:

• a black square
• a white square
• a black circle
• a white circle

Someone tells you: "I have secretly picked one color (either black or white) and one shape (either square or circle). A symbol is called a THOG if it has exactly one of the properties I picked."

Then, they give you a big clue: "The black circle is a THOG."

Your job is to figure out for the other three symbols (the white square, the black square, and the white circle) if they are:

• a) definitely a THOG,
• b) impossible to tell, or
• c) definitely not a THOG.

Why is This Puzzle Tricky?

This puzzle can be hard because you need to hold a lot of information in your mind at once. Our working memory (the part of your brain that holds information you're actively thinking about) can get overloaded. It's like trying to juggle too many balls!

How to Solve the THOG Problem

Let's break down the puzzle step by step. The most important clue is: "The black circle is a THOG."

This means the black circle has exactly one of the properties the experimenter picked.

Figuring Out the Secret Properties

Since the black circle is a THOG, the secret properties picked by the experimenter cannot be:

• Black and Circle: If these were the secret properties, the black circle would have *both* (black AND circle). But a THOG only has *one* property. So, this is wrong.
• White and Square: If these were the secret properties, the black circle would have *zero* of them. But a THOG has *one* property. So, this is also wrong.

This leaves us with only two possible pairs of secret properties:

• Possibility 1: The secret properties are Black and Square.

* Let's check the black circle: It has 'black' (one property), but not 'square'. So, it has exactly one property. This works!

• Possibility 2: The secret properties are White and Circle.

* Let's check the black circle: It has 'circle' (one property), but not 'white'. So, it has exactly one property. This also works!

So, the secret properties are either (Black and Square) OR (White and Circle).

Testing Each Symbol

Now, let's test each of the other symbols using these two possibilities.

The White Square

• If the secret properties are Black and Square:

* The white square has 'square' (one property), but not 'black'. * It has exactly one property, so it's a THOG.

• If the secret properties are White and Circle:

* The white square has 'white' (one property), but not 'circle'. * It has exactly one property, so it's a THOG.

Since the white square is a THOG in BOTH possible situations, the white square is definitely a THOG.

The Black Square

• If the secret properties are Black and Square:

* The black square has 'black' AND 'square' (two properties). * It does NOT have exactly one property, so it's NOT a THOG.

• If the secret properties are White and Circle:

* The black square has 'black' and 'square'. It has zero of the chosen properties (white or circle). * It does NOT have exactly one property, so it's NOT a THOG.

Since the black square is NOT a THOG in BOTH possible situations, the black square is definitely not a THOG.

The White Circle

• If the secret properties are Black and Square:

* The white circle has 'white' and 'circle'. It has zero of the chosen properties (black or square). * It does NOT have exactly one property, so it's NOT a THOG.

• If the secret properties are White and Circle:

* The white circle has 'white' AND 'circle' (two properties). * It does NOT have exactly one property, so it's NOT a THOG.

Since the white circle is NOT a THOG in BOTH possible situations, the white circle is definitely not a THOG.

The Answer

Here is the final answer to the THOG problem:

• The white square is definitely a THOG.
• The black square is definitely not a THOG.
• The white circle is definitely not a THOG.

This puzzle shows how careful thinking and breaking down a problem can help solve even the trickiest logic challenges!