# Frank Morgan's Math Chat - ONCE IN A MILLENNIUM

OLD \$200 DOUBLE BUBBLE CHALLENGE. The best response comes from John Snygg, who seems to have a computatonal proof of the conjecture for the special case of A large. The undergraduate research Geometry Group had proofs for A = 1 and for A small. The general case remains of much interest, since it would simplify certain arguments in proving the Double Bubble Conjecture (which says that the familiar double soap bubble is the least-area way to enclose and separate two given volumes of air). There are rumors that a proof of the conjecture may be announced soon.

NEW CHALLENGE "Once in a Millennium" (David Shay). The year 2000 can be represented as the sum of consecutive integers:

2000 = 398 + 399 + 400 + 401 + 402.

The year 2001 can be represented as the sum of consecutive integers:

2001 = 1000 + 1001.

In fact, every year in the millennium from 2000 to 2999 can be represented as the sum of consecutive integers, except one year. Which year cannot be represented as the sum of consecutive integers?

Send answers, comments, and new questions by email to [email protected], to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.