Take out a piece of paper and a pencil, I am going to ask you to write some letters in your sheet of paper and then I am going to challenge you to fold the sheet of paper... with a twist!
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Setup
Seriously though, please take out a piece of paper and lay it out horizontally (or in "landscape mode", were the piece of paper a mobile device).
Now I need you to crease your sheet of paper in half, along a horizontal line; then I need you to crease it in half along a vertical line, and then in half again, along a vertical line.
In the end, you should have your piece of paper creased like this:
Except that your creases should be nicely centered, unlike the drawing I made... Oh well!
Problem statement
Now the challenge is the following: I am going to ask you to write the letters ABCDEFGH in the rectangles you created and I need you to fold the piece of paper in such a way that,
- the eight small rectangles are on top of each other, making a stack of eight squares of paper;
- if you go through the rectangles one at a time, the letters show up in order.
The only restriction is that you can't cut your sheet of paper! The point is to fold it, not to take a pair of scissors and cut the paper along the creases.
There are going to be three levels, corresponding to three different letter layouts in the rectangles you creased. Start with level 1, write down the letters and try to fold the paper correctly. When you get it right, erase the letters and write down the letters for level 2, and then for level 3! Good luck!
Level 1
Level 2
Level 3
Give it some thought... and most important of all, try it for real with an actual piece of paper! Let me know how it went in the comment section below ;)
Tip: if you are having a hard time keeping track of which rectangle is which, consider also writing the letters on the back of the sheet of paper, but be sure to label them correctly; a single rectangle should have the same letter front and back!
Tip: if the paper is too strong and you are having a hard time manipulating it, consider scrambling it and then flattening again before continuing.
I heard of these from a friend and he learned about this problem by watching this YouTube video.
Solution
You can read the solution here to compare with your own solution.
If you liked this article and would like to support the mathspp project, then you may want to buy me a slice of pizza 🍕.
