Hundred-dollar, Hundred-digit Challenge problems


The Hundred-dollar, Hundred-digit Challenge problems are 10 problems in numerical mathematics published in 2002 by. A $100 prize was offered to whoever produced the most accurate solutions, measured up to 10 significant digits. The deadline for the contest was May 20, 2002. In the end, 20 teams solved all of the problems perfectly within the required precision, and an anonymous donor aided in producing the required prize monies. The challenge and its solutions were described in detail in the book.

The problems

From :
  2. A photon moving at speed 1 in the xy-plane starts at t = 0 at = heading due east. Around every integer lattice point in the plane, a circular mirror of radius 1/3 has been erected. How far from the origin is the photon at t = 10?
  3. The infinite matrix A with entries is a bounded operator on. What is ?
  4. What is the global minimum of the function
  5. Let, where is the gamma function, and let be the cubic polynomial that best approximates on the unit disk in the supremum norm. What is ?
  6. A flea starts at on the infinite 2D integer lattice and executes a biased random walk: At each step it hops north or south with probability, east with probability, and west with probability. The probability that the flea returns to sometime during its wanderings is. What is ?
  7. Let A be the 20000×20000 matrix whose entries are zero everywhere except for the primes 2, 3, 5, 7,..., 224737 along the main diagonal and the number 1 in all the positions with. What is the entry of ?
  8. A square plate is at temperature. At time, the temperature is increased to along one of the four sides while being held at along the other three sides, and heat then flows into the plate according to. When does the temperature reach at the center of the plate?
  9. The integral depends on the parameter α. What is the value of α in at which I achieves its maximum?
  10. A particle at the center of a 10×1 rectangle undergoes Brownian motion till it hits the boundary. What is the probability that it hits at one of the ends rather than at one of the sides?

    Solutions

  11. 0.3233674316
  12. 0.9952629194
  13. 1.274224152
  14. −3.306868647
  15. 0.2143352345
  16. 0.06191395447
  17. 0.7250783462
  18. 0.4240113870
  19. 0.7859336743
  20. 3.837587979 × 10−7
These answers have been assigned the identifiers,,,,,,,,, and in the On-Line Encyclopedia of Integer Sequences.