Problems

The following problems are printed in the February 1998 issue. Solutions will be printed in future issues.
Solutions for theses problems should be mailed before May 31, 1998. (Solutions sent after that date will be considered as deadlines permit.)

4645-S: Student Problem - only undergraduate and pre-college students are eligible to submit a solution.
Proposed by Joe Dan Austin, Houston, TX.

4646-OBG: Oldie But Goodie
Proposed by H.C. McMillin, Washington, KS.

4647: Proposed by Richard L. Francis, Cape Girardeau, MO.

4648: Proposed by Richard L. Francis, Cape Girardeau, MO.
A power triangle is an oblique (non-right) triangle whose side measures are integers and whose area is an exact power (square, cube, etc.). Show that the set of power triangles is infinite.

4649: Proposed by Roger Izard, Dallas, TX.
Berta and Bert have been playing 3-game matches of pool for a long time. They would play 3 games and whoever won the majority of the games would win the match. One day Bert said to Berta: "Look, you are a much better player than I am. Instead of playing 3-game matches, let's play 5-game matches. Then my chances of winning a match will be twice as good as they are now." How much better a player is Berta than Bert? In other words, find the probability of Bert's winning a single game.

4650: Proposed by Murray S. Klamkin, Edmonton, Alberta, Canada.
If a rectangular hyperbola and a circle intersect in four points, prove that the segment joining the centers of the two curves is bisected by the centroid of the four points of intersection.
Note: For a related problem, see Problem 4548-S in the Solutions section.

4651: Proposed by Khiem V. (Thomas) Ngo, Falls Church, VA.