Springs and Strings
John P. Robertson
Spring A and Spring B are identical coil springs, each of whose length is proportional to the force acting on it. The top of Spring A is attached to the ceiling. A 10" cord hangs from the bottom of Spring A, connecting it to the top of Spring B. A 10-lb. weight is attached to the bottom of Spring B. Initially each spring is stretched to 10" in length, so the weight is 30" from the ceiling. There are also two other cords, each 21" long, one attached to the ceiling and to the top of Spring B, and the other attached to the bottom of Spring A and the top of the weight. These two cords are slack initially. The 10" cord is cut. The weight starts bobbing up and down, and eventually comes to rest. How far from the ceiling is it?
The object of last issue's game was to maneuver chess pieces in a certain diagram so that four white bishops traded places with four black bishops, with no captures possible during the transfer. Assign numbers to the squares, starting in the upper left corner, and going across rows, so the first row is 1 to 5, the second is 6 to 10, etc. Walter Fransen interchanged the bishops on the white squares by making the moves 6-12, 20-2, 10-14, 12-4, 2-6, 14-18, 16-8, 8-20, 4-8, 18-10, 6-18, 8-2, 10-4, 18-12, 2-14, 12-6, 4-16, 14-10. This takes 18 moves. Similarly, the bishops on the black squares can be interchanged in 18 moves. A solution was also submitted by John Herder.