Logic Puzzles | How to Solve a Logic Puzzle

If you're new to grid-based logic puzzles, this tutorial will teach you the basics. Start with the "Introduction" first, then move on to the tutorials discussing specific clues or solving methods. Each tutorial contains a number of different slides - you can advance to the next slide by clicking "Next slide" at the bottom of each page, or by using the circled numerical links below each slide. Choose your specific tutorial from the list below to get started.

Slide #1

Transpositions are an essential part of solving a logic puzzle. In fact, this is without a doubt the one solving method you will use more than any other. It is a grid-only solving method, meaning you do not need to reference any clues when using it.

What is a transposition? Simply put, it's a graphical representation of one of the two most basic rules of logic:

1. If A is equal to B, and B is equal to C, then A is equal to C.

2. If A is equal to B, and B is not equal to C, then A is not equal to C.

We'll use this grid to demonstrate several transpositions.

Next slide »
Slide #2

Whenever you place a new true value anywhere on the grid, the first thing you should do after placing it is to see whether or not a transposition can be made between the two items in that true relationship.

Here's an example. The current grid shows that Isaac's tattoo cost $45. It also shows (via the row shaded in yellow) that the $45 tattoo is not (1) pink, (2) Aquarius, (3) Gemini or (4) Virgo.

Using just that information, can you see where four transpositions can be made on the grid?

« Prev slide »Next slide »
Slide #3

Since we know that Isaac == $45, we can take the four false relationships already known for $45 and transpose them directly into Isaac's column. Therefore:

1. Isaac is not Aquarius.

2. Isaac is not Gemini.

3. Isaac is not Virgo.

4. Isaac is not pink.

« Prev slide »Next slide »
Slide #4

Continuing with the exact same grid, there are still more transpositions that can be made.

Look at the row shaded in yellow. Can you determine what transpositions can be placed thanks to the data in that row?

« Prev slide »Next slide »
Slide #5

If Virgo == pink, then all of the false relationships we already have for pink can be transposed for Virgo as well.

Therefore, since Virgo isn't Kendra or Zachary:

1. Pink cannot be Kendra.

2. Pink cannot be Zachary.

« Prev slide »Next slide »
Slide #6

But wait... there's more!

Two additional false relationships can be transposed thanks to the Virgo == pink true relationship. Can you find them?

« Prev slide »Next slide »
Slide #7

Look at the column shaded in yellow.

If Virgo == pink, and pink doesn't equal $55 or $60, then we can transpose false relationships for Virgo and $55, and Virgo and $60.

« Prev slide »Next slide »
Slide #8

So far we've shown several examples of false transpositions - but there are true transpositions as well.

Here we've kept the same grid as before, only now we've marked a third true value. We now know that pink == $40.

Do you see where the true transposition can be placed?

« Prev slide »Next slide »
Slide #9

Look again at the column for "pink" (shaded in yellow). It now has two true relationships:

1. Pink == $40

2. Pink == Virgo

If Pink == $40, and Pink == Virgo, what does that tell us?

« Prev slide »Next slide »
Slide #10

Basic logic dictates that if A equals B, and B equals C, then A must equal C.

Therefore, if pink == $40, and pink == Virgo, then Virgo must equal $40. We can transpose a true value to the box where Virgo and $40 intersect.

We'll end the lesson here, but for extra credit, there are now two new false transpositions that can be made on the grid. See if you can find them!

(Hint: they involve Kendra and Zachary, in relation to price.)

« Prev slide »

How to Solve a Logic Puzzle

Transpositions