# Tricky Paper Puzzle

prosoccer
Posers and Puzzles 26 Jun '06 20:45
1. 26 Jun '06 20:45
Here is the situation, you are at the post office, preparing to mail your tax return. You see a man in front of you carrying his, and you notice something strange as he is preparing to put his sheets in a folder. He has one of his pages cut into thirds, one third he puts into his pocket, the other he gives to a clerk, and the other he mails off.

You go up to the man to tell him about his mistake. You argue fiercely, but learn that the page is supposed to be cut like that, at the insistence of the man and others around you.

A man at the counter allows you to borrow his scissors, but tells you that you can only cut one, straight cut, before the scissors disintegrate. You aren't allowed to tear the page that you need to cut(for the reasons of the government), nor can you borrow any sort of cutting tool or ripping tool from anyone else (you don't have any suitable device on your body either).

The tax return must be mailed off within only a few minutes if you hope to get it off in time, and your wife will be enraged with you if you go outside without having mailed it.

How can you cut the desired sheet into thirds, with only one slice by the scissors? I am not looking for a technical aspect, just something general.

P.S. I am sure you people will come up with some out of the box solutions (e.g. juggling bridge puzzle), but I am really only looking for one answer.
2. 26 Jun '06 20:48
you fold it so that with one cut it will be in thirds
3. 26 Jun '06 20:51
Originally posted by ajte
you fold it so that with one cut it will be in thirds
It's supposed to take more time than this!
4. 26 Jun '06 20:53
am i right?!?!
5. 26 Jun '06 20:55
yes
6. 26 Jun '06 20:56
that was quick!
7. 26 Jun '06 21:16
and how would you fold it?
what about cutting the page into ten equal pieces
ten UNEQUAL pieces?
n UNEQUAL pieces?
8. 26 Jun '06 23:30
you could of course "score" in the two other places
9. 26 Jun '06 23:30
You do a tri-fold, that is you move both edges away from each other but towards the folds that the other edge is making??? Crease the page lightly, then unfold. Refold the paper in half (the creases should align perfectly, if not, redo the first fold). Cut along the lined-up creases. This will yield 3 equi-sized pieces.

The question is: If the page was 8.5" by 11" how many non-equal sized squares could you cut out of the page so that the whole page has been made into squares? For language definition: A square has 4 equal lengthed sides and four equal angle corners. A rectangle is NOT a square.
10. 27 Jun '06 02:01
Originally posted by Gastel
You do a tri-fold, that is you move both edges away from each other but towards the folds that the other edge is making??? Crease the page lightly, then unfold. Refold the paper in half (the creases should align perfectly, if not, redo the first fold). Cut along the lined-up creases. This will yield 3 equi-sized pieces.

The question is: If the page wa ...[text shortened]... square has 4 equal lengthed sides and four equal angle corners. A rectangle is NOT a square.
But a square is a rectangle.
11. 27 Jun '06 03:41
Originally posted by prosoccer
But a square is a rectangle.
His statement was partially correct. ALL rectangles are not squares.
12. 27 Jun '06 13:59
Originally posted by hypothetical
His statement was partially correct. ALL rectangles are not squares.
I realise that; my statement is correct too.
13. 27 Jun '06 18:41
Originally posted by prosoccer
I realise that; my statement is correct too.
True... my goof. I meant "Not all rectangles are squares... therefore use only shapes that can be called squares."
14. Suzianne
Misfit Queen
28 Jun '06 22:093 edits
Originally posted by prosoccer
Here is the situation, you are at the post office, preparing to mail your tax return. You see a man in front of you carrying his, and you notice something strange as he is preparing to put his sheets in a folder. He has one of his pages cut into thirds, one third he puts into his pocket, the other he gives to a clerk, and the other he mails off.

You go the box solutions (e.g. juggling bridge puzzle), but I am really only looking for one answer.
You can also roll up the sheet so that the circumference of the cylinder is equal to one-third the length of the sheet. (Or, just make sure the cylinder is made from exactly three revolutions as you are rolling it up.) Then cut through the cylinder length-wise right where the top of the sheet is. (That should also be right where the bottom of the sheet is (on the inside of the cylinder though).)

Sorry, the answer "you fold it so that with one cut it will be in thirds" doesn't get it... it merely restates the problem, it doesn't say exactly "how" to fold the paper. Also, I'm not exactly what you would call "dim", but I can't figure out Gastel's instructions either.

Okay, last edit, I swear! Maybe I *am* dim, because I suddenly figured out Gastel's instructions. Well done.
15. 29 Jun '06 00:00
Originally posted by Suzianne
...Okay, last edit, I swear! Maybe I *am* dim, because I suddenly figured out Gastel's instructions. Well done.
Don't worry, it took me three times reading it before I understood it too!