# Census Challenges

Old census challenge

Gordon Squire notes that planners for the 2000 US Census wonder what to do about missing certain groups of people such as the homeless in New York. Suggestions include statistical random sampling. What approach would you suggest?

Answer

Two interesting suggestions came from students calling the MathChat cable-TV show in Williamstown, Mass. Second-grader Nicholas de Veaux proposed basing the census on the phone book. Of course, there is usually just one name per family, some phones are not listed, and some folks (such as the homeless) have no phones. Third-grader Eli Raffeld suggested announcing that anyone could register family and friends at town hall and get $10 per registration. For the United States, which has a population of about 260 million, that could cost $2.6 billion, which is almost exactly what the census did cost in 1990.

Heath Dill reasoned that since he was one person in a 100-square-foot room, and the area of the US is about 100 trillion square feet, the population of the US must be about a trillion (1000 billion).

Robert Lewis, who actually spent two years homeless in New York, writes: "I can tell you one thing homeless persons all have in common. They eat." He suggests requiring census registration to eat at food distribution centers. Joseph Huberman would enter everyone who registers in a million dollar lottery.

Regular solids

There are five regular solids: (1) the cube with its six square faces, (2) the tetrahedron with its four triangular faces, (3) the octahedron with its eight triangular faces, (4) the icosahedron with its 20 triangular faces, and (5) the dodecahedron with its 12 five-sided faces. What are the regular solids in higher dimensions?

Answer

The first three of the above regular solids generalize to all higher dimensions: (1) the hypercube, (2) the generalized tetrahedron or "regular simplex," and (3) the generalized octahedron or "cross polytope" or "orthoplex." That is it, except for four-dimensional space, where all five generalize and a sixth appears, the "24-cell."

New 'four 4s' challenge (Howard Sheldon)

How far can you get in forming numbers 0, 1, 2, 3, ... from four 4s and the standard mathematical operations +, -, x, /, decimal point, square root, powers, and factorial(!)? For example, 0 = 4+4-4-4 and 1 = 44/44. Sheldon says he got up to 30. How far can you get?

* Send answers and new questions to:

Math Chat; Bronfman Science Center; Williams College; Williamstown, MA 01267

or Frank.Morgan@williams.edu