Ponder This
Friday, July 1st, 2005IBM Research has put up the July challenge on their Ponder This site.
Update: Here is the problem:
Upon a rectangular table of finite dimensions L by W, we place n identical, circular coins; some of the coins may be not entirely on the table, and some may overlap. The placement is such that no new coin can be added (with its center on the table) without overlapping one of the old coins. Prove that the entire surface of the table can be covered completely by 4n coins.