Help with empty boxesalgorithmic problem.

  • Thread starter atwarwithmaths
  • Start date
  • Tags
    Empty
In summary, the problem involves filling eleven large boxes with unknown numbers of medium and small boxes. The end result is 102 empty boxes and the task is to determine the total number of boxes. The solution involves finding an invariant and using a semi-brute force method to solve for the number of boxes. One possible invariant is n+m, which represents the number of boxes filled in the first and second steps.
  • #1
atwarwithmaths
6
0
Hi, I've been given this problem for homework but I am completely baffled..I can't even translate the first move into values on the variables..

Any help on this would be greatly appreciated..Sorry if I'm being a bit abrupt here but my head is fried at this stage..

Thanks Guys..


Homework Statement



Eleven large empty boxes are placed on a table. An unknown number of the boxes is selected and, into each, eight medium boxes are placed. An unknown number of the medium boxes is selected and, into each, eight small boxes are placed.

At the end of this process there are 102 empty boxes. How many boxes are there in total?


Homework Equations


The Attempt at a Solution



Variables:
e = number of empty boxes
f = number of full boxes

Initial Values:
e=11
f=0
 
Physics news on Phys.org
  • #2
The maximum number of boxes total is 11*8*8 if we put 8 medium boxes into all 11 of the boxes then 8 small boxes into all of the medium boxes.

Notice the largest number of boxes disappear if we leave a large box empty.

The best way I could see to do it is semi-brute force. Basically taking out medium boxes until your empty boxes is less than 102. Then use the same method for the medium, and the small.
 
  • #3
Thanks for the quick reply Feldoh,

I like what you're saying..it makes sense but I have to come up with an invariant. If I don't then I will get no marks at all
 
  • #4
Suppose you fill n boxes on the first step and m boxes on the second. Carefully count the number of empty boxes as a function of m and n. You'll find the number of empty boxes only depends on n+m. Since it equals 102, you can solve for n+m. Now, carefully count the total number of boxes. You'll find it also depends only on n+m. Not all choices of n and m give a solution, but those that do always give the same total number of boxes. I think.
 
Last edited:
  • #5
I think I may be getting it.. what variables would you introduce then?

n: number of boxes
e: number of empty boxes

I need to discover an invariant for this.

I've tried modelling a move: fill 1 box

e:= e+7
n:=n+8

what possible invariants can I get from this? TBH I'm not sure if I even understnad what an invariant is and this is due in tommorrow
 
  • #6
n=number of large boxes filled. m=number of medium boxes filled. What's the TOTAL number of boxes (in terms of n and m)?
 
  • #7
n+m? I'm lost?
 
  • #8
11 large boxes. n larges boxes filled, so 8*n medium boxes. m medium boxes filled, so 8*m small boxes. What's the total? Now count how many are empty. I'll get you started. 11-n large boxes are empty. How many medium boxes are empty and how many small boxes are empty? What's that total?
 

1. What is an empty boxes algorithmic problem?

An empty boxes algorithmic problem is a mathematical or computational problem that involves filling up a certain number of empty boxes with a specific set of objects according to a set of rules or constraints.

2. What are some common real-life applications of empty boxes algorithmic problems?

Empty boxes algorithmic problems can be used to solve real-life problems such as scheduling tasks, optimizing resource allocation, or designing efficient transportation routes.

3. How do you approach solving an empty boxes algorithmic problem?

To solve an empty boxes algorithmic problem, you need to carefully analyze the problem and its constraints, determine the appropriate algorithm or method to use, and then implement and test your solution.

4. What are some common challenges when solving an empty boxes algorithmic problem?

Some common challenges when solving an empty boxes algorithmic problem include dealing with complex or changing constraints, ensuring that the solution is efficient and optimal, and handling large amounts of data or variables.

5. Are there any resources or tools that can help with solving empty boxes algorithmic problems?

Yes, there are many resources and tools available such as textbooks, online courses, and programming languages specifically designed for solving algorithmic problems. It can also be helpful to collaborate with other researchers or use online forums to discuss and get feedback on your approach.

Similar threads

  • Engineering and Comp Sci Homework Help
2
Replies
55
Views
6K
  • Introductory Physics Homework Help
Replies
5
Views
4K
  • Precalculus Mathematics Homework Help
Replies
10
Views
3K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
Replies
7
Views
539
  • Precalculus Mathematics Homework Help
Replies
10
Views
2K
  • Electrical Engineering
3
Replies
83
Views
3K
  • Precalculus Mathematics Homework Help
Replies
14
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Replies
13
Views
1K
Back
Top