The Chicken From Minsk: Extra Circumference from Additional Diameter

The scientists at Los Alamos, New Mexico working on The Manhatan Project which created the weapon that would end World War II, had a lot of time on their hands in the evenings. They chose to spend their time creating math puzzles. My favorite on is The Chicken From Minsk. Here is a summary:

An international company laid a fiber-optic cable completely encircling the Earth, by chance running through a new, privately owned chicken farm in the city of Minsk (the capital of Belarus). The chickens refuse to walk or fly over the cable and will only pass under it. The cable must be raised off the ground by 1 foot if the chickens are to survive. For technical reasons, the cable must then be raised 1 foot higher everywhere around the entire circumference of the Earth (the cable is thick and fragile and cannot be bent or twisted, even slightly). The farmer refuses to permit the cable to cross his land unless it is raised. The company agrees to raise the cable only if the farmer agrees to pay for all of the additional cable, at the rate of $1 per foot. The farmer agrees, provided that the company will pay for the additional supporting structures. These supporting structures (one foot long) have to be placed each eighth of a mile, at a cost of $1 per support. How much will the chicken farmer pay for the additional cable? Try this before you read on.

The attached pdf has a graphic that shows the circumference of the Earth at approximately 25,000 miles after we look at the diameter of the Earth at approximately 8,000 miles. I even added a graphic that showed the additional diameter created by the problem of 2 feet. Since last week we learned that the relationship between diameter and circumference is always a factor of pi or approximately 3 1/7 or 3.14, we simply multiply the extra 2 feet of  diameter by 3 1/7 and generate additional circumference of 6 2/7 feet. It is so counter intuitive to think that the farmer must pay for only that little additional cable to raise it 1 foot around the entire planet and pay $6.28. I made the challenge a little more interesting by stating that the company agreed to put 8 supports per mile around the Earth to raise the cable at a cost of $1 per support. Of course, the company had to spend $200,000 (8 x 25,000) and thought the additional cable cost would be much more than $6.28.

Then we discussed what if the cable had to be raised more than one foot, such as 5 feet. So, the diameter would have increased 10 feet and multiplying by an approximation of pi we get 31 3/7 feet of additional cable.

The worksheet challenges the children to double the radius to get diameter and then multiply by pi but they were able to see the pattern quickly that all they had to do was to count by 3 1/7. I challenged some of the 3rd graders and all of the 4-7th graders to use both 3 1/7 and 3.14. Pages 3-5 of the pdf are for the 1st and 2nd graders. Pages 6-8 of the pdf add the element of 3.14 for grades 3 and up.

Have fun sharing the Chicken from Minsk puzzle and see how many people can generate the solution. This is not one of those puzzles where you can make an educated guess; you either see the additional diameter and multiply by pi or you don’t. By the way, try this on another planet like Jupiter with a circumference 1,000 times bigger than Earth and the solution is still an additional 6 2/7 feet of cable.