Old Mt. Everest Challenge
Although Mt. Everest, at 29,028 feet above sea level, is the highest mountain in the world, it is not the farthest from the center of the earth. The earth's bulge at the equator pushes Chimborazo in Ecuador, at 20,561 feet above sea level, farther. (How much?) Now suppose you run a water pipe from Everest to Chimborazo. Which way would the water flow?
Although it seems hard at first to determine water-level equilibrium on a bulging earth, the ocean does that for us!
Since Everest is higher above sea level, the water would flow from Everest to Chimborazo.
Jim Henry remarks that such a pipe along the ground would be more than 10,000 miles long and that the pressure at sea level would be more than 800 times atmospheric pressure.
Dave Rossum and Greg Sahagen also compute that Chimborazo is about 7,000 feet farther from the center of the earth than Everest.
An ancient king requires that each of his 10 chieftains pay him tribute of 2,000 10-gram gold coins. He learns that one of them plans to use counterfeit 9-gram coins, but he does not know which one. He has an accurate scale that reads out exact weight.
How many weighings does he need to identify the cheater? What if there may be any number of cheaters?
* Send answers, comments, and new questions to our sabbatical address:
Dr. Frank Morgan
1921 Lehigh Parkway North
Allentown, PA 18103
or by e-mail to: Frank.Morgan@williams.edu to be eligible for Flatland and other book awards.
Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan, from which you can access previous columns and his Math Chat TV show.
We especially recommend the March 9 show, featuring elementary school winners of his Soap Bubble Geometry Contest.
Note to Readers: After a two- year run of informative puzzlement we will no longer be publishing Math Chat. Our sincere thanks to Professor Morgan.
The next column on Oct. 1 will be the last.