The Human Cannonball Riddle: Can You Solve It?

Imagine yourself as the human cannonball, a thrilling act involving flying through rings of fire, bouncing across trampolines, and a daring catch with a trapeze artist. But what happens when sabotage threatens the entire performance? Let's dive into this intriguing puzzle and see if you can solve it in time!

The Premise

Your cannon, powered by metal coils, is designed to launch you at the perfect speed. However, a pre-flight test reveals a critical issue: someone has tampered with the power settings, pushing them to the maximum. With the clock ticking and the trapeze artist's safety on the line, you must act fast to fix the cannon.

The Cannon's Configuration

The cannon, a creation of your eccentric mentor, operates with energy cells housed in 16 chambers across two levels. Each level forms a hollowed-out square with three chambers per side. To ensure a survivable launch, certain conditions must be met:

• The upper level must contain twice as many energy cells as the lower level.
• Each chamber can hold between 1 and 3 energy cells.
• Each side of the cannon (comprising 6 chambers) must have a total of 11 energy cells.

Adding to the complexity, the original shipment of energy cells was short by three. Your mentor adjusted the configuration to work with this reduced number, achieving a perfect launch. Your task is to replicate this configuration using the correct number of energy cells in the right places.

Cracking the Code: Solving the Riddle

Narrowing Down the Options

Let's start by focusing on the third rule: each side of the cannon must have 11 energy cells. If we place 11 cells in two corners, we might only need 22 cells in total. Conversely, placing 11 cells in the middle chambers could require as many as 44 cells. Therefore, the answer must fall within this range.

Refining with Additional Rules

Considering that the upper level has twice as many cells as the lower level, the total number of cells must be a multiple of 3. Additionally, we need to find two consecutive multiples of 3 that satisfy all conditions.

Applying the 1-to-3 Cell Rule

Each chamber can only contain 1 to 3 cells. This means the lower level must have at least 8 cells, making the upper level 16. However, this configuration doesn't work because if two opposite sides had 8 cells, the upper level's entire capacity would be used, leaving no cells for the remaining chambers. Thus, 24 cells is not a viable solution.

Exploring the Extremes

The upper level can have a maximum of 3 times 8, or 24 cells, resulting in a total of 36 cells. However, with 36 cells, each chamber would need to have 3 cells, meaning each side of the upper level would already have 9 of its 11 cells. This would require empty chambers on the lower level, making 36 an unsuitable option.

The Process of Elimination

What about 33 cells? If we place 2s at opposite corners of the upper level, we would have 8 of the required 11 cells per side. Placing exactly 1 cell in each lower chamber would fall short of the lower level's required 11 cells. This leaves us with two options: 30 and 27. By process of elimination, 27 must be the correct number.

The Solution: 27 Energy Cells

To total 9, the lower level must have seven 1s and one 2. Placing the 2 in a middle chamber would result in too many cells in the upper level. Therefore, the 2 must go into a corner. The upper level can then be arranged accordingly.

The Mystery of the Sabotage

With the last energy cell snapped into place, you hear the ringleader announcing your act. But amidst the chaos, you've also gathered enough clues to solve another mystery: Who sabotaged your cannon? That's a riddle for another time!

Can you solve the human cannonball riddle? Share your thoughts and solutions in the comments below!