A Sheet of Stamps

[ujjagrawal]

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.

[bonanova]

Gotta ask: does the size of the grid matter?

Or should we assume m by n?

[ujjagrawal]

Gotta ask: does the size of the grid matter?

Or should we assume m by n?

I am looking for a general answer.

[altuss]

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

[bhramarraj]

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

[curr3nt]

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

edit - nevermind, you could do a fan fold.

Edited June 25, 2012 by curr3nt

[EventHorizon]

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

).

[EventHorizon]

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.

[phil1882]

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.