Tricky Logic Puzzle (IV): How To Really Solve It? - An illustration showing a row five turned-on light bulbs. Beside this row, a robot named "Cheat" appears to be in a puzzled state.

Welcome to the fourth entry in the tricky logic puzzle series. This time, we have just “Cheat” the robot with us. As you can see in the title image, we have a row of five turned-on light bulbs.

Furthermore, Cheat makes the following statement:

Tricky Logic Puzzle (IV): How To Really Solve It? — An illustration showing the robot “Cheat” saying, “Every switched-off light bulb is next to at least one more switched-off light bulb”.
Cheat’s statement — Illustrative art created by the author

Given this initial setting, your challenge is to figure out a light bulb (on-off) configuration for the entire row which satisfies the following conditions:

1. An even number of light bulbs are turned on.

2. Cheat is lying.

3. Every turned-on light bulb is next to at least one more that is turned on.

4. The fourth light bulb from the left is turned off.

Please note that liars in this puzzle ALWAYS lie. Also, the final light bulb (on-off) configuration MUST satisfy all of the above statements. Do you think you can solve this?

Spoiler Alert

If you wish to solve this puzzle independently on your own, I suggest that you pause reading this essay at this point. Beyond this section, I will be explicitly discussing the solution to this puzzle.

After you are done with your attempt, you may continue reading and compare our respective logics and the final solution.

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Setting Up the Tricky Logic Puzzle — Eliminating Possibilities

The trick to this puzzle is NOT to look for the final light bulb configuration but to eliminate possibilities step by step. When you take a look at the list of conditions we must satisfy, you will notice that the fourth point directly gives us a light bulb we can turn off.

Consequently, we arrive at the following configuration:

Tricky Logic Puzzle (IV): How To Really Solve It? — An illustration showing a series of five light bulbs. Of the five light bulbs, the fourth one from the left is switched off. The rest are turned on.
Fourth light bulb turned off — Illustrative art created by the author

As the next logical step, we could check this configuration against our list of conditions to see how many we satisfy as follows:

1. An even number of light bulbs are turned on — Satisfied.

2. Cheat is lying â€” Satisfied.

3. Every turned-on light bulb is next to at least one more that is turned on â€” NOT satisfied.

4. The fourth light bulb from the left is turned off â€” Satisfied.

Condition number 3 is not yet satisfied because the right-most bulb is not next to another light bulb that is turned on. To rectify this situation, we may choose to turn the right-most light bulb off:

Tricky Logic Puzzle (IV): How To Really Solve It? — An illustration showing a series of five light bulbs. Of the five light bulbs, the last two from the left are switched off. The rest are turned on.
Last two light bulbs turned off — Illustrative art created by the author

Consequently, we now have an odd number of light bulbs turned on. Furthermore, Cheat’s original statement becomes true again, because both bulbs that are switched off are next to each other:

1. An even number of light bulbs are turned on â€” NOT Satisfied.

2. Cheat is lying â€” Not Satisfied.

3. Every turned-on light bulb is next to at least one more that is turned on â€” Satisfied.

4. The fourth light bulb from the left is turned off â€” Satisfied.

It may not look like it, but we are very close to solving the puzzle. Let us take a look at our final consideration(s).

The Solution to the Tricky Logic Puzzle

If we switch off one more light bulb, we have an even number of turned-on light bulbs again. The question is: which one should we turn off? To answer that question, we need to consider Cheat’s statement.

Tricky Logic Puzzle (IV): How To Really Solve It? — An illustration showing a series of five light bulbs. Of the five light bulbs, the last three from the left are switched off. The rest are turned on. Above the row is an explicit sign saying that this configuration is incorrect.
Last three light bulbs turned off — Illustrative art created by the author

If we choose to turn off the third light bulb from the left, we end up in a situation where all the turned-off light bulbs are next to each other. This would make it impossible for Cheat’s statement to be a lie. So, the light bulb we turn off next cannot be the third from the left.

Tricky Logic Puzzle (IV): How To Really Solve It? — An illustration showing a series of five light bulbs. Of the five light bulbs, the first and the third from the left are turned on. The rest are turned off. Above the row is an explicit sign saying that this configuration is incorrect.
Light bulbs 2, 3, and 5 turned off — Illustrative art created by the author

If we choose to turn off the second light bulb from the left, the first and the third light bulbs (from the left) would not be directly next to any light bulbs that are also turned on. This would in turn violate our third requirement.

Tricky Logic Puzzle (IV): How To Really Solve It? — An illustration showing a series of five light bulbs. Of the five light bulbs, the first, fourth, and fifth ones from the left are switched off. The rest are turned on. Above the row is an explicit sign (tick mark) saying that this configuration is correct. Beside the row of light bulbs, the robot Cheat is seen saying, “You have NOT solved the puzzles.” As we already know, Cheat is lying.
The solution (final configuration) — Illustrative art created by the author

So, we have no other option other than to switch off the first light bulb. This configuration satisfies ALL of our conditions.

1. An even number of light bulbs are turned on â€” Satisfied.

2. Cheat is lying â€” Satisfied.

3. Every turned-on light bulb is next to at least one more that is turned on â€” Satisfied.

4. The fourth light bulb from the left is turned off â€” Satisfied.

If we turn one more light bulb off, we end up with an odd number of turned-on light bulbs again. If we turn both light bulbs off, Cheat’s statement becomes true again.

Therefore, the working configuration we have is the ONLY unique solution possible for this puzzle.

I hope you enjoyed solving this logic puzzle. I will try to work on more logic puzzles and keep this series going. So, keep an eye out if you are interested!

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Further reading that might interest you:

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