Postage Stamps - May 13-17, 1996
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Fold a block of eight postage stamps, as indicated below, along the perforations and without tearing, so as to form a single pile with the stamps numbered consecutively from top to bottom.
Annie says: Solutions
This is a fun problem, and I get the feeling that a lot of you had a good time with it.
I have given credit to three people who did something that I figure is physically impossible, but their teacher wrote to attest to the fact that it worked. Basically they did a bunch of folds and then turned the whole thing inside out. I accepted it, mostly because I couldn't get the "real" solution to work with stamps (too humid here, for one thing - the stamps got sticky), and they said they had used a whole sheet of paper. It's probably a good idea, though, to try out your solution on the actual objects named in the problem. A whole sheet of paper is a lot more flexible than a bunch of stamps.
Explaining this problem might just be harder than figuring it out in the first place. Two people (from different schools, from opposite ends of the country) used the same phrase to describe their initial style - "hot dog style." It's a great phrase, and it's pretty cool that two people used it! A number of people used the idea of forming a circle with the 7 on the outside. That really helps get the idea of the loop.
When doing a problem like this, there are certainly occupational hazards you need to be aware of - a couple of people complained about paper cuts!
Following are some highlighted solutions. The names of all the people who submitted correct solutions and most of the solutions are also available. We have several new schools this week, including one from Singapore.
Sarah Fisher and Shannon Foss Grades: Freshman and Junior School: Ridgeview High School --------------------------------- | | | | | | 6 | 3 | 5 | 4 | | | | | | | | | | | --------------------------------- | | | | | | | | | | | 7 | 2 | 8 | 1 | | | | | | --------------------------------- First, fold the stamps so the 4 is under the 1. Then wrap the 7 in between the 1 and 4 and continue to push it over until the 7 is in between the 8 and 6 and the 2 is in between the 1 and 3. By doing that correctly you will have a single pile of the stamps in consecutive order from top to bottom.
Tan Li Ling and Tor Xue Ling Grade: Grade 7 School: Raffles Girls' School (Singapore) Step 1: Number both sides of the paper. Step 2: Fold it into half along the length. The numbers '6 3 5 4' should be facing you. Step 3: Tuck '7' and '6' between '1' and '4' from the front. Push it further in until '7' and '6' is between '8' and '5'. The '2' and '3' should be between '1' and '4' now.
Carly Tubbs Grade 9 Fairfield High School, Fairfield, CT Fold the stamps in half, hot dog style. Put the side with 7, 2, 8, 1 facing you. Take the lefthand side and bring it around to meet the righthand side. Put the lefthand side between the 1 and 4. Slide the lefthand side through the two halves until it can't go any further. There should be a stack now the size of a postage stamp.
Bilal Seyal Grade 9 Fairfield High School, Fairfield, CT First I took the paper and folded it the long way so that all of the numbers were facing out. I then put the one and seven together so that a circular prism, without the bases, was formed. Then I opened up the "pocket" of the one and I slid the other end with the seven in. I kept sliding it until the two was under the one. After this was done, all the numbers were lined up from one to eight in the right order.
Thomas S. Kuo Grade: 7 School: Murray Junior High School, Ridgecrest, California (1) Fold in half (lengthwise) * * * * * * * * * * * * * * 7 * 2 * 8 * 1 * * (6) * (3) * (5) * (4) * Number in () is number in the back * * * * * * * * * * * * * (2) Cut 2/3 of line between 1 and 8. They are still attached. (3) Fold 7, 2, 8 to the back of 1 along line between 1 and 8 * * * * * * * * * * * 1 * 3 * 6 * * * (2) * (7) * * * * * * * * * * * (4,5,8) (4) Fold 3 and 6 along line between 1 and 3 and put between face 1 and 4. * * * * * * * * 7 * 1 * * (6) * * * * * * * * * (2,3,4,5,8) (5) Fold 7 along line between 1 and 7 and put between 5 and 8. * * * * * 1 * * * * * * * (2,3,4,5,6,7,8) (6) They are in sequence now.
Dave Peterson Homeschool math teacher, Grade 5 Rochester, New York I am a software engineer at ABB, and a homeschool math teacher. My son hasn't figured this one out yet, but I like it enough to make this my first submission after several weeks of just watching. I assume the question involves "mathematical" stamps - no thickness, and infinitely flexible, not rigid rectangles that must remain planar throughout the process; my solution comes very close to breaking the rules. To get the required configuration in the 3x5 sheet of paper I used for my attempts, I had to do a lot of bending and twisting, not just folding along the "perforations" while keeping the "stamps" flat. Once I did that, the hardest part became how to describe what I did! The idea is to fold lengthwise, so 7, 2, 8, 1 remain on the front with a fold along the top; then curl this around the back, sticking the 7 end inside the 1 end until the 7 is under the 8 (on the back) and the 2 is under the 1 (on the front). When this spiral is tucked in fully and flattened out, the numbers are in order (with some upside down). Here is an attempt to draw what I did. First, the strip after the first fold, as seen from the front: ________________________________________________________________ / / / / /\ | | | | | | | | | | | | | 7 | 2 | 8 | 1 | 4| | | | | | | | | | | |__| |_______________|_______________|_______________|_______________| and as seen from the bottom (so you can see both edges): Front _______7_______________2_______________8_______________1_______ | | | | | |_______6_______|_______3_______|_______5_______|_______4_______| | Back | +-----> Now curl this around to the back, without tucking in yet, still looking from the bottom: _____________1___________ / ____________4___________| / / __________2_______________ /_/ / _________3______________ \ \ \ \_\________6___________ \_\ \ \ \_________7___________| / / \ \___________5_____________/ / \____________8______________/ Now, open the spiral back up and repeat the curl, but this time tuck it between the front and back so the 2/3 pair is inside the 1/4, and the 6/7 pair is inside the 5/8: ______________1___________ / ____________2___________|___ / / ___________3___________|__ \ / /_/ _________4___________| \_\ \ \ \ \________5______________/ / \ \ \__________6___________ / \ \___________7___________| / \_____________8_____________/
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