Securing n Sheets with Thumbtacks: Can You Prove My Conjecture?”

  • MHB
  • Thread starter mrtwhs
  • Start date
  • Tags
    Conjecture
In summary, the minimum number of thumbtacks needed to secure n sheets of paper on an infinitely large bulletin board is 2n. This is based on the assumption that all four corners of each sheet can be secured with one thumbtack, allowing for slightly overlapping sheets. A conjecture for the formula 2n is proposed, but a proof has not yet been determined.
  • #1
mrtwhs
47
0
You have an infinite supply of square sheets of paper. You are going to secure these sheets on an infinitely large bulletin board by using thumbtacks. You must secure all four corners of each sheet however you may slightly overlap the sheets so that one thumbtack could secure up to four sheets at once. Under these assumptions, one sheet requires 4 tacks, 2 sheets require 6 tacks, 3 sheets require 8 tacks, etc.

What is the minimum number of thumbtacks needed to secure \(\displaystyle n\) sheets?

I have a conjecture for a formula but have no clue how to prove it.
 
Mathematics news on Phys.org
  • #2
Here is my conjecture for the number of thumbtacks needed for \(\displaystyle n\) sheets of paper.

\(\displaystyle T(n) = \lceil(1+\sqrt{n})^2 \rceil\) where the upper brackets represent the ceiling function.
 

1. What is the purpose of securing n sheets with thumbtacks?

The purpose of securing n sheets with thumbtacks is to provide a method for keeping multiple sheets of paper together in a secure and organized manner. This can be useful for tasks such as creating a booklet or binding important documents.

2. How does securing n sheets with thumbtacks work?

Securing n sheets with thumbtacks involves placing a thumbtack through the top left corner of a stack of sheets, and then repeating this process for each subsequent sheet. The thumbtacks hold the sheets together and allow for easy flipping through the pages.

3. Can thumbtacks be used to secure more than n sheets?

It is possible to use thumbtacks to secure more than n sheets, but the number of sheets that can be secured may be limited by the size and strength of the thumbtacks. It is important to use a sufficient number of thumbtacks to prevent the sheets from slipping or becoming disorganized.

4. Can you prove the conjecture that securing n sheets with thumbtacks is a reliable method?

As a scientist, I must rely on evidence and experimentation to prove or disprove a conjecture. While the use of thumbtacks to secure n sheets may be a commonly accepted method, further research and testing would be needed to provide a definitive proof of its reliability.

5. Are there any potential drawbacks or limitations to securing n sheets with thumbtacks?

One potential drawback to securing n sheets with thumbtacks is that the thumbtacks may create holes in the sheets of paper. Additionally, if the number of sheets being secured is too large, the thumbtacks may not be strong enough to hold them together effectively. It is also important to note that thumbtacks are not a permanent form of binding and may not be suitable for long-term use.

Similar threads

Where's the flaw in this proof of the Collatz Conjecture?
    • General Math
Replies
5
Views
3K
I Can New Theorems Predict Incomplete 5x5 Magic Square Solutions?
    • General Math
2
Replies
68
Views
9K
I Can chatgpt accurately calculate expected lengths in Pascal's triangle?
    • General Math
2
Replies
66
Views
4K
I Karatsuba multiplication implementation question
    • General Math
Replies
3
Views
1K
How to compute flexure and failure loads of acrylic sheets
    • Materials and Chemical Engineering
Replies
4
Views
13K
Reverse polarity protection circuit. Help with component values?
    • Electrical Engineering
Replies
17
Views
10K
Relationship between constructibility of reg. polygons and cot(pi/N)
    • General Math
Replies
1
Views
2K
Conjecture: There exists no number k s.t. k^2+2 is a multiple of 7
    • Linear and Abstract Algebra
Replies
5
Views
3K
The Folding Challenge - how low can your ratio go?
    • General Engineering
Replies
3
Views
5K
A The double copy of (2,0) theory
    • Beyond the Standard Models
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top