Rock bands often stack their speakers in an array. One teen band has 24 speakers. They stack them at least 2 high, but no taller than 8 high. What are all the different arrays they can make.
2*12
3*8
4*6
6*4
8*3
To determine all the different arrays that the teen band can make with their 24 speakers, we can use a combination of loops and conditional statements. Let's break down the problem and explain the steps to get the answer:
1. Define the range: We know that the speakers can be stacked at least 2 high and no taller than 8 high. This gives us a range of possible heights between 2 and 8 inclusive.
2. Iterate through the possible heights: We will use a loop to iterate through each possible height within the defined range.
3. Find the number of possible arrays at each height: For each height, we need to find the number of arrays that can be made. Since the total number of speakers is fixed at 24, the number of speakers stacked at a given height should be a divisor of 24. So, we need to find all the divisors of 24.
4. Count the number of arrays: We will use another loop within the loop from step 2, going through all the divisors of 24. For each divisor, we will calculate the number of possible arrays based on the height and the divisor.
Here's one way to implement this solution using Python:
```python
total_speakers = 24
# Iterate through each possible height
for height in range(2, 9):
print("Height:", height)
print("Arrays:")
# Find all the divisors of 24
divisors = []
for divisor in range(1, total_speakers + 1):
if total_speakers % divisor == 0:
divisors.append(divisor)
# Count the number of arrays for each divisor
for divisor in divisors:
if divisor <= height:
width = total_speakers // divisor
print(" ", divisor, "x", width)
print()
```
By running this code, you will get the different arrays that the teen band can make with their 24 speakers, based on the given conditions.
24x1
12x2
8x3
6x4