**Stephanie’s Cubical Puzzle: Unraveling the Mystery**

Imagine yourself staring at a box filled with 30 uniform cubes. You’re tasked with arranging them in a way that leaves enough space for one more cube. It’s a puzzle that can leave your mind tangled and your frustrations rising.

**The Struggle with Cube Organization**

Organizing cubes can be a daunting task, especially when space is limited. You spend hours trying different configurations, only to end up with a jumbled mess. The frustration of not finding the perfect fit can be overwhelming, making you want to give up.

**The Solution: A Simple Yet Effective Method**

The key to solving Stephanie’s cubical puzzle lies in a simple but effective method. By breaking down the cubes into smaller units and using a systematic approach, you can create a structure that accommodates all 30 cubes and leaves room for one more. This method is not only efficient but also allows you to visualize the solution more clearly.

**Summary: Organizing Cubes Mastered**

In summary, Stephanie’s cubical puzzle requires a step-by-step approach, where you break down the problem into smaller units. By utilizing this method, you can organize 30 cubes in a box and leave space for one more. Whether you’re a seasoned organizer or a novice, mastering this technique will empower you to tackle any cubical challenge with confidence.

## Stephanie’s Cubical Conundrum

Stephanie embarked on a mission to organize her cherished collection of 30 cubes. With meticulous precision, she arranged these cubic wonders into a rectangular box, seeking the most efficient configuration.

### Dimensions and Volume

The box measured a modest 3 units in length, 2 units in width, and 5 units in height, resulting in a volumetric capacity of 30 cubic units. This neatly accommodated the 30 cubes, each boasting a unit volume.

### Single-Layer Configuration

To maximize space utilization, Stephanie initially opted for a single-layer arrangement. She aligned the cubes in a rectangular pattern, forming a 5-by-6 grid. This configuration occupied the entire base of the box.

### Two-Layer Configuration

However, a clever idea emerged. By stacking three cubes vertically, Stephanie created a second layer. This layer comprised four stacks of three cubes each, resulting in a 2-by-4 grid.

### Maximizing Vertical Space

With two layers in place, Stephanie realized the remaining space in the box could be utilized more effectively. She carefully stacked three more cubes on top of each stack in the second layer.

### Final Configuration

After meticulously stacking and arranging the cubes, Stephanie achieved her optimal configuration. The box now contained four layers with the following arrangement:

- Bottom layer: 5-by-6 grid
- Second layer: 2-by-4 grid
- Third layer: 2-by-4 grid with three cubes stacked on each
- Top layer: three cubes stacked on each of the four bottom stacks

### Conclusion

Through a series of thoughtful arrangements, Stephanie successfully packed 30 cubes into a box in the most efficient configuration. By considering dimensions, volume, and vertical space, she devised a clever solution that maximized the box’s capacity.

## FAQs

**How many cubes did Stephanie pack in the box?**

- 30

**What were the dimensions of the box?**

- 3 units in length, 2 units in width, and 5 units in height

**What was the volume of the box?**

- 30 cubic units

**What was the optimal arrangement of the cubes?**

- Four layers, with a 5-by-6 grid at the bottom, a 2-by-4 grid with three cubes stacked on each in the middle two layers, and three cubes stacked on each of the four bottom stacks on the top layer

**What was the motivation for Stephanie’s careful arrangement of the cubes?**

- To maximize space utilization and efficiency

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Stephanie,Puts,Cubes