The Story Behind the Puzzle

On a lovely Sunday afternoon, three friends—Matt, a human; Can, a puppy; and Cheat, a robot—are enjoying some leisure time in their garden. Cheat, especially, is delighted to have a break after undergoing rigorous logic training to perfect his skills.

However, their peaceful day is interrupted when a mysterious alien spaceship appears out of nowhere, capturing Cheat with a tractor beam. Matt and Can can only watch in disbelief as their friend is taken away.

Not long after, another alien ship arrives, and in a shocking turn of events, it also captures Matt and Can.

An Unexpected Challenge Awaits

Upon arriving on the alien ship, Matt and Can are greeted by a peculiar extraterrestrial. The alien explains their predicament:

“We wish to assess the intelligence of humans. You may communicate one-way with your metallic companion, who is held captive in another spaceship by a force field. Your friend will receive three clues to deduce a passcode that will free him. You must convey the correct passcode based on what you hear.”

Realizing they have no choice, Matt and Can prepare to listen closely to Cheat’s audio feed.

Cheat's Challenge Begins

Meanwhile, Cheat is briefed by another alien, who provides him with the first clue:

1. The product of the three digits in your passcode is 36.

After contemplating this, Cheat asks for the second clue, which is:

2. The sum of the digits equals the number of logic problems you have solved today.

Matt and Can, eavesdropping on this exchange, grow anxious, knowing Cheat has crucial information they lack. The alien then shares the third clue:

3. The largest digit appears only once in the passcode.

As moments pass, they hear a series of beeps followed by the activation of a tractor beam. The alien announces that Cheat has successfully figured out the passcode.

Now, it's your turn to solve the mystery! Can you determine the passcode and the reasoning that Matt and Can used to arrive at their conclusion?

Spoiler Alert

This section will discuss the solution, so if you want to attempt it yourself, pause here.

Hint (Optional)

Consider why Cheat couldn't arrive at the passcode after the second clue.

Setting Up the Logic Puzzle

Let’s summarize Cheat’s clues into mathematical expressions involving variables (x), (y), and (z) (where (x leq y leq z)):

1. (x cdot y cdot z = 36)
2. (x + y + z = text{Number of logic problems solved by Cheat})
3. (z) is unique, meaning (z neq x) and (z neq y).

Assembling the Puzzle Pieces

Reflecting on the hint, it seems Cheat needed the third clue for sufficient information. Once he received it, he could narrow down the possibilities.

To solve the puzzle, we need to identify all potential combinations of numbers that multiply to 36:

Now we calculate the sums of these combinations:

We look for combinations that yield the same sum, as Cheat was considering multiple options before receiving the third clue. The candidates with matching sums are [1, 6, 6] and [2, 2, 9].

Applying the Third Clue

The third clue specifies that the largest number must be unique. In the combination [1, 6, 6], the number 6 appears twice. However, in [2, 2, 9], the number 9 is unique!

Thus, the correct passcode is [2, 2, 9]. I hope you enjoyed solving this puzzle. Stay tuned for more logic puzzles in the future!

Update Post Publishing

A keen reader pointed out that some combinations could be disregarded since they don't adhere to the single-digit condition. This leaves us with only five valid combinations to choose from.

The first video, "How to Solve a Logic Puzzle," provides insights on tackling similar puzzles, enhancing your problem-solving skills.

The second video, "6 Glasses - Logic Puzzle with Second Alternative Answer," presents a brain teaser that further challenges your logic skills.