Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #26 2007-11-08 03:09:55

Dross
Power Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

I think quiet appreciation is enough.

## #27 2007-11-08 20:36:08

JohnnyReinB
Power Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

ok, Then lets quietly celebrate?

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

## #28 2007-12-12 16:11:46

Kargoneth
Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

#### John E. Franklin wrote:

I am dumb;  can you have a 1-dimensional rectangle of paper for the frame with zero area?

An interesting question . A rectangle is a two-dimensional object though

I believe the quote below is very similar to what you are visualizing (just using molecules as the frame).

#### JohnnyReinB wrote:

I think, for any sized paper, the largest hole you can cut (without doing the tricks of turning it into a hole with a larger area than the original) is one with one with an edges thickness of an  atom/molecule's diameter. The percentage differs from paper to paper, so I don't know the percentage...if you destroy the atoms/molecules when cutting the paper, the paper would break down, and it would no longer be paper with a hole in it! It would just be a bunch of subatomic particles.

Agreed. It could also be worded that the instant you destroy one of the molecules making up the perimiter of said paper, the paper would become a string/sheet 1 atom wide, without a hole (since it has essentially gone from a ring to a rod, lol)

#### Anthony.R.Brown wrote:

Paper! as you know it!.. is not the Paper Known in the Enormous! World of Infinity!...

*Scratches head* Um... exclamation marks aside, what do you mean 'world of infinity'? That makes no sense.

Last edited by Kargoneth (2007-12-12 16:15:42)

## #29 2007-12-12 21:30:53

JohnnyReinB
Power Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

My point exactly...

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

## #30 2008-01-12 09:12:26

LuisRodg
Real Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Could anyone explain the trick of "making the hole larger than the paper"? I do not understand it.

## #31 2008-01-12 16:53:28

JohnnyReinB
Power Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

you cut it zigzaggedly

i---------------i
l  ________   l
l_______   l   l
l  ________l  l
l  l   _______l
l  l_______    l
'---------------'

If, you cut it like that, it would open the paper up, and now you created a hole with a larger size than the original paper.

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

## #32 2008-01-13 01:25:39

John E. Franklin
Star Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Wow!  I gotta try that!  Be back...

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #33 2008-01-13 01:32:58

John E. Franklin
Star Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

That's totally awesome!!!  The first one I made I missed the two side cuts in and I ripped it apart.
Then I looked at yours again and made a new one with the zigzag and two cuts off the sides.
It really does get like twice the size of a piece of paper!!!   Hexagonal and twisty frame.

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #34 2008-01-13 17:12:22

JohnnyReinB
Power Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

In fact, the more times you cut it (by making the spaces between zigs and zags narrower) you can make it larger and larger, which returns us to the main topic of this, uhm, topic.

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

## #35 2008-03-16 13:54:08

simron
Real Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Shall we assume that this is not 3-dimentional matter, but a 2-dimentional plane segment? Therefore, the limit of the percentage of the paper consumed by the hole (no zigzaggedy lines) is 100%. But it cannot be 100%. Unless you warp the quantum mechanical stuffage. Any tips?

Linux FTW

## #36 2009-06-18 20:43:49

RickyIsAnIdiot
Banned

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

For simron
Quote:

But it cannot be 100%. Unless you warp the quantum mechanical stuffage. Any tips?

RickyIsAnIdiot

The Hole! cannot be 100% So 99.999...% has to be the Size of the Hole! There must always be some Paper around the Outside!.

## #37 2009-06-20 03:41:27

soroban
Power Member

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Hello, everyone!

Someone already explained the "trick" to this classic puzzle.

It is usually given in a variety of forms:
. . "Cut a hole in a standard playing card so that it will fit over your head."
. . "Cut a hole in a sheet of typing paper so that you can walk through it."

Fold the paper lengthwise.

#### Code:

```      *-----------------------*
|                       |
|                       |
|                       |
|                       |
|                       |
* - - - - - - - - - - - * ← fold```

.

Along the fold, make several cuts across the paper
. . but not all the way across.

#### Code:

```      *-----------------------*
|                       |
|   |       |       |   |
|   |       |       |   |
|   |       |       |   |
|   |       |       |   |
* - * - - - * - - - * - *```

.

Along the outside edge make several cuts between the first cuts,
. . again, not all the way across.

#### Code:

```      *-------*-------*-------*
|       |       |       |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |       |       |   |
* - * - - - * - - - * - *```

.

Cut along the fold between the first and last cuts.

#### Code:

```      *-------*-------*-------*
|       |       |       |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |       |       |   |
* - *-------*-------* - *
: ← ←  cut  → → :```

.

Unfold the paper carefully.
You will have a "ring" of paper.

The ring can be made larger by applying more cuts.
.

## #38 2009-06-20 22:55:36

RickyIsAnIdiot
Banned

Offline

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

For soroban above!...

Can you tell me what Percent the Hole is! and what Percent the Paper is!

RickyIsAnIdiot