Stationary Suns and Kings and Queens

Old Planet X challenge question:

My friend on Planet X reports that the sun stayed at the same spot on the horizon for a whole 24-hour day. How can this be?

Answer:

The planet's axis of rotation is horizontal, not vertical. Two days a year, it points directly at the sun, which appears to hang directly over the North or South Pole. If our friend lives on the equator, he sees it stationary on the horizon.

Chuck Gahr remarks that Uranus's axis is almost horizontal, so that a resident on the equator would see the sun stationary for the (17-hour) day twice every orbit (about 84 Earth-years).

Ruth Gatto points out that the Bible says our sun once stood still at the Lord's command (Joshua 10:12-14).

Winners for correct answer and best explanations: Roger Bliss, John Brandt, Daniel Cebada, Timothy Clark, Jim Eagle, Charles Gahr, Ruth Gatto, John Kruschke, Alice Loth, Cory Pihl.

Challenge question

(Thanks to Daniel Cebada.)

A magician takes a stack of eight cards (four kings and four queens, face down, in some order), turns the top one face up, moves the next one to the bottom of the stack, turns the next one face up, moves the next one to the bottom, and so on. To deal out an alternating sequence of four kings and four queens, how must he arrange the cards beforehand? Suppose instead he has some number of cards, each with a letter of the alphabet. Can you arrange them to spell out some word or phrase, which also spells out another word or phrase?

Send answers and new questions to:

Math Chat

Bronfman Science Center Williams College Williamstown, MA 01267

or by e-mail to: Frank.Morgan@williams.edu

*Frank Morgan is a professor of mathematics at Williams College