IBM has a monthly Ponder This page, with questions and solutions dating back to 1998. There is still time to get your name on the top 100 solvers.

Challenge for September 2005 is

Ponder This Challenge:
Puzzle for September 2005.

This puzzle was sent in by Alan O'Donnell.
It comes in three parts; solve as many as you can.

Part 1:
You have a frictionless pulley with a rope over it. On one side is a 3kg weight. On the other side is a weightless frictionless pulley with another rope over it. This second pulley has a 1kg weight on one side, and a 2kg weight on the other. You have a frictionless pulley with a rope over it; the pulley is attached to an immovable ceiling.

At what rate (in terms of g, the acceleration due to gravity) does the 3kg weight accelerate downwards when the system is released?

Part 2:
Suppose the system described in Part 1 is on one end of a rope over another pulley, with a 6kg weight on the other side. How fast does the 6kg weight accelerate in terms of g?

Part 3:
Suppose this sequence is continued with weights 1kg, 2kg, 3kg, 6kg, 12kg, 24kg, ..., 3*(2**m)kg. What is the general term for the acceleration of the heaviest object?




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The first 100 people who answer all three parts correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!