Sign in to follow this  
Followers 0

A Sheet of Stamps

9 posts in this topic

Posted · Report post

Sunny has a sheet of stamps that he wants to separate into individual stamps. How can he do it with the fewest possible tears? Assume the stamps are all rectangular, all the same size, arranged in a uniform rectangular grid, each stamp is perforated along all 4 edges, and the sheet is very thin.

0

Share this post


Link to post
Share on other sites

Posted · Report post

Gotta ask: does the size of the grid matter?

Or should we assume m by n?

0

Share this post


Link to post
Share on other sites

Posted · Report post

Gotta ask: does the size of the grid matter?

Or should we assume m by n?

I am looking for a general answer.
0

Share this post


Link to post
Share on other sites

Posted · Report post

4 times maximum, if size is more than 3*3. Fold till you get strip 2 stamps wide and tear to half. You will get a lot of 2 stamps wide strips. Place strips one above othear and tar again. A lot of 1 stapm strips. And now fold strips same way and after 2 tears you will have seperate stamps

1

Share this post


Link to post
Share on other sites

Posted · Report post

I also agree to altuss. It will take 4 number tears to separate each stamp.... same applies for 3X3 size also.

0

Share this post


Link to post
Share on other sites

Posted (edited) · Report post

Even a thin piece of paper has a finite number of possible folds...

edit - nevermind, you could do a fan fold.

Edited by curr3nt
0

Share this post


Link to post
Share on other sites

Posted · Report post

One tear. Explanation to come (wanted to post answer first

:) ).
0

Share this post


Link to post
Share on other sites

Posted · Report post

First, make the stamps square. Make however many fan-like folds necessary to have them end up square, being careful not to have the fan folds large enough to overlap into the area of another stamp. (Notice that the stamps need not all be the same size initially, just that the perforation needs to always be aligned rectilinearly and along the whole sheet. You would just end up needing to make all the stamps a square the size of the smallest individual length of perforation (whether it is a height or width of a stamp). This means you could have made the puzzle even harder

:) )

Second, fan along the diagonal. Fold the top left stamp in half forwards diagonally (top left corner to bottom right). Then you will make a backwards fold that goes along the diagonal that goes through the two stamps touching that stamp (the stamp one to the right and the stamp one down). Continue through the whole sheet. This will leave you with something that looks like the following (but with 45 and 90 degree angles):

|\

| \

|  \

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/
Third, fold again using a fan-like method as shown in the diagram below, alternating forwards and backwards folds.
|\

| \

|  \

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/


to

 ___ <--folded back

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/


to

 ___ <--folded forward

|\  |

| \ |

|__\|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/


to

 ___ <--folded back

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/


to

 ___ <-- folded forward

|\  |

| \ |

|__\|

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/


to

 ___ <-- folded back

|  /|

| / |

|/  |

|\  |

| \ |

|  \|

|  /

| /

|/


to

 ___ <-- folded forward

|\  |

| \ |

|__\|

|  /

| /

|/


to


 ___ <--folded back

|  /|

| / |

|/__|

Now all the perforation and only the perforation is along that diagonal... so letta rip.

1

Share this post


Link to post
Share on other sites

Posted · Report post

i think the best you can do if you are not allowed to fold is log[2](m*n).

take the example of 8 by 16.

tear in half. so you now have two 8 by 8 squares.

place the two under each other and tear in half. you now have four 4 by 8 sheets.

and so on.

0

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now
Sign in to follow this  
Followers 0

  • Recently Browsing   0 members

    No registered users viewing this page.