Solving 5-Stone Counting Problem w/ Restrictions

In summary, there are 72 possible arrangements of 5 differently colored stones (red, orange, blue, green, purple) if the green stone cannot be placed at the front or the back of the sequence. This is because if the green stone is placed in the second, third, or fourth position, there are 3 possible arrangements for the other 4 stones. Therefore, the total number of arrangements is 3 x 3 x 3 = 27. Since there are 3 possible placements for the green stone, this number is multiplied by 3, resulting in a total of 27 x 3 = 81 arrangements. However, the book says the answer is 72, so we can assume that the remaining 9
  • #1
lesquestions
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Hi, I wasn't sure how to approach this problem:

You have 5 differently colored stones-red, orange, blue, green, purple. If the green stone cannot be placed at the front or the back of the sequence, how many possible arrangements can you make?

I know that without the above restriction, the amount would be 5!=120.

But I don't get how to use the restriction.

BTW the back of the book says that the answer is 72.

Help please! thanks.
 
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  • #2
How many ways can you place the green one, then place the rest?

P.S. please don't multiple post.
 
  • #3
um 3? lol I don't get it...
 
  • #4
The DO it.

Suppose you place the green stone in the second place. How many different ways are there to place the other 4 stones?

Suppose you place the green stone in the third place. How many different ways are there to place the other 4 stones?

Suppose you place the green stone in the fourth place. How many different ways are there to place the other 4 stones?

Okay, now how many ways is that all together?
 

Related to Solving 5-Stone Counting Problem w/ Restrictions

1. What is the 5-Stone Counting Problem with Restrictions?

The 5-Stone Counting Problem with Restrictions is a mathematical problem that involves arranging five stones in a specific pattern with certain restrictions. The goal is to find all possible arrangements of the stones that meet the restrictions.

2. What are the restrictions in the 5-Stone Counting Problem?

The restrictions in the 5-Stone Counting Problem can vary, but some common restrictions include: the stones must be arranged in a straight line, there must be an even number of stones on each side of the center stone, and the stones must be arranged in a specific color pattern.

3. How is the 5-Stone Counting Problem solved?

The 5-Stone Counting Problem can be solved by using a combination of logic and trial-and-error. First, the restrictions must be carefully considered and a plan for arranging the stones must be developed. Then, the possible arrangements can be tested until the correct solution is found.

4. What is the purpose of solving the 5-Stone Counting Problem?

The 5-Stone Counting Problem is a common exercise used in mathematics and logic to test problem-solving skills. It also helps to develop critical thinking and spatial reasoning abilities. Additionally, solving this problem can have practical applications in fields such as computer science and engineering.

5. Are there any real-world applications of the 5-Stone Counting Problem?

Yes, the 5-Stone Counting Problem has real-world applications in fields such as computer science and engineering. It can be used to optimize computer algorithms and design efficient systems. Additionally, the problem can be applied to various physical systems, such as arranging objects in a specific pattern for maximum stability.

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