The text contains over 1700 challenges. For some challenge solutions of particular didactic or research value I offer special prizes. In addition, I'll add the first good solution I receive to the free physics textbook, together with the sender's name. To apply for a prize, mail a solution to christoph@motionmountain.net. The prizes currently offered are the following:
Challenge 9 (August 2009): Determine how the probability of belt-trick-like rotation for a polymer-tethered ball depends on the radius of the ball and the number of polymer chains. The length of the polymers is assumed very large compared to all other dimensions. (Prize value: 50 euro)
No attempt so far. Prize not yet awarded.
Challenge 8 (July 2008): Explain the problems in performing a Bohm-type experiment with two nuclei that are first near each other and then separated. (Prize value: 50 euro)
No attempt so far. Prize not yet awarded.
Challenge 7 (May 2007): Taking a combined photograph of a rainbow, similar to the one by Stefan Zeiger, but including a third segment with the ultraviolet picture. (Prize value: 50 euro)
No attempt so far. Prize not yet awarded.
Challenge 6 (October 2006): Extending the belt trick to spin 3/2 (suggested by Frank Sheldon). The Dirac belt trick simulates the behaviour of a spin 1/2 particle. What is the construction for a composed spin 3/2 particle? For an elementary spin 3/2 particle? (Prize value: 50 euro)
1 attempt so far. Prize not yet awarded.
Challenge 5 (April 2006): The simplest unsolved knot problem. Imagine an ideally wobbly rope, that is, a rope that has the same radius everywhere, but whose curvature can be changed as one prefers. Tie a trefoil knot into the rope. By how much do the ends of the rope get nearer? In 2006, there are only numerical estimates for the answer: about 10.1 diameters. There is no formula giving the number 10.1 yet - can you find one? Alternatively, solve the following problem: what is the rope length of a closed trefoil knot? Also in this case, only numerical values are known -- about 16.33 rope diameters -- but no exact formula. (Prize value: 200 euro)
1 attempt so far. Prize not yet awarded.
Challenge 4 (January 2006): Rotation in special relativity. Make a movie of a sphere/football with relativistic speed and relativistic rotation speed. Show the strange effects that appear. (Prize value: 200 euro)
Half an attempt so far. Prize not yet awarded.
Challenge 3 (April 2005): Classical Lagrangian for waves. Use the relation for the errors in angular frequency and time for wave packets, dw dt > 1/2, to show that the classical action for a wave is bounded below. Find the precise bound by assuming that the initial and final points for which the action is determined must themselves obey the wave packet relation. (Prize value: 150 euro)
No attempts so far. Prize not yet awarded.
Challenge 2 (April 2005): The 'tangles inside a sphere' problem. This problem combines topology, combinatorics and geometry. Find the number of topologically different tangles that can fit into a sphere of given volume, with the assumption that every strand, though flexible, has constant diameter. A glass sphere of radius R contains n strands of diameter d (d<R), all starting and ending on the surface (at 2n given and fixed points distributed over the surface). How many topologically different tangles can be formed, under the condition that the diameter d has the largest possible value for a given n? [Note: in mathematics, one distinguishes trivial, composed, rational, locally knotted and prime tangles. The problem asks for the number of possible tangles that are composed or prime. Locally knotted tangles may be left out of the counting; rational tangles do not count as topologically different in this problem.] (Prize value now raised to 1000 euro; the solution should be published.)
1 attempt so far. Prize not yet awarded.
Challenge 1 (January 2005, now solved): The parking problem. Find the minimum number of times one has to drive backwards and forwards to leave from a parking space, when the available space and the geometry of the car are given. Look up the details by searching for 'car parking' in the book index. (Prize value: 50 euro)
After several attempts by others, in May 2007 the prize has been
awarded to Daniel Hawkins.
Each prize will be awarded to the first person to mail a full or reasonably full solution. Partial prizes may also be awarded.