As one travels the surface of the earth during ones life, what percent of the time is one antipodal to water? For US residents, the answer is likely to be (nearly) 100 per cent; Hawaii is antipodal to Namibia, southern America to China, and New Zealand to Spain, but little else of consequence. There is a website, www.antipodemap.com, which shows one's antipodal point in considerable detail.
People in High Places
There exist a handful of US cities, towns, and villages for which it is true that there are no places simultaneously higher in elevation and with a larger population: New York, Chicago, Denver. Colorado Springs, Santa Fe, Laramie (WY), Los Alamos (NM), Alamosa (CO), Gunnison (CO), Leadville (CO), Alma Park (CO). What is the corresponding list of populated places for the world? It is difficult to ascertain population and elevation for small settlements in Peru, Bolivia, and Tibet, but such a list begins with Tokyo, Mexico City, La Paz, Potosi Bolivia, Cerro de Pasco Peru, and (possibly) Junin Bolivia or Jiachan Tibet. The 1997 Guinness cites a settlement on the T'e-Li-Mi Trail in Tibet at an altitude of 19,750 feet. Very likely the highest settlements are mining camps, but whether these should be counted as permanent settlements is doubtful.
Triple Points on Maps
Each US state has a boundary containing one or more triple points where two other states adjoin (UT, NM, AZ, and CO have a quadruple point). Tennessee has the most triple points (8); what US county has the most triple points? Fulton County, GA, west of Atlanta, is a candidate with 10 triple points. What is the distribution function of triple (or quadruple) points for US counties (ie, what fraction of counties have 3, 4, 5. . .triple points?)
How would the states appear if each state were allowed only that land that is closer to its state capital than to any other state capital? The western end of Virginia is closer to 9 other state capitals (those of WV, OH, IN, KY, TN, NC, SC, GA, and AL).
Areas Surrounded by Traffic Lights
For most of the US, it is true that one can travel from one point to another in such a way that no traffic lights are encountered. However, the area inside cities is not included; for any point in a city, one must traverse at least n lights before the traffic-light-free region is reached. The larger the city, the larger the value of n; what is the largest town in the US for which there is no inaccessible region? (For the Green in the center of Morristown, the number appears to be 2.) How close can you approach a city before a traffic light must be encountered? In my own experience, my home in Morris Township is in the traffic-light-free region, but one cannot approach New York City closer than Summit, NJ.
A. Ross Eckler was editor and publisher of Word Ways from 1968 to 2006 and has written some 300 articles for this quarterly journal, plus three books on wordplay (Word Recreations, Dover 1979; Names and Games, University Press of America 1986; Making the Alphabet Dance, St. Martin's Press 1996). In addition he wrote the privately published book The National Puzzlers' League: The First 115 Years, published in 1998. He is a member of the latter organization and served as president (1985) and editor of their monthly newsletter, The Enigma (1986-88). He received a BA from Swarthmore College in 1950 and a PhD from Princeton University in 1954 in Mathematics and, professionally, was a member of the technical staff as well as department head at Bell Telephone Laboratories 1954-84, consulting with engineers in the fields of statistics and probability (and has an Erdos Number of 2). His past and present avocational interests include ballet, evaluation of extreme human longevity, genealogy and Herkimer County NY local history, hiking, caving, NY-NJ boundary history, and carillon.
copyright © 2008, A. Ross Eckler
BECCA DE LA ROSA
—The Baby is Safe
—The Fisherman's Child
—Faith, Hidden in the Hands of the Blind
—A Comic History of Bullets
—To Recover from Lightning, Etc.
A. ROSS ECKLER