[Suggested by W. Martin] Find the center of a given circle using only a double-edged straight edge (unmarked ruler with edges parallel and width less than the diameter of the circle). [Suggested by W. Martin] Find the number n so that the equation KYOTO + KYOTO + KYOTO = TOKYO has a solution in the base-n number system. Each letter is to represent a particular digit, and different letters represent different digits. [Suggested by I. Kornfeld] The distance from a point P to a given line l is the length of the shortest line segment that you an draw starting at P and ending on l. (Draw a line q that passes through P and is perpendicular to l . Let Q be the intersection of l and q. The distance from P to Q is equal to the distance from P to l.) Consider an equilateral triangle. Pick a point P inside this triangle. Show that the sum of the three distances from P to the sides of the triangle is always the same regardless of the position of the point. In fact it is equal to the length of the side of the triangle. [Suggested by N. Barabanov] Four dogs may run along the sides of a square, and one wolf may run everywhere on the plain. At the starting moment the wolf is sitting in the middle of the square and the dogs sit in all the corners. The maximal speed of each dog is equal to 1.5 times maximal speed of the wolf. The wolf wants to go outside the square, while the dogs want to prevent it. If meeting, wolf eats one dog immediately, but two dogs, while meeting the wolf, kill it also at once. Can the dogs run in such a way (depending on the motion of the wolf) that to prevent the wolf to go outside the square. Problems will be due on November 15, 2004. Check www.ndsu.edu/math/talent for solutions and more problems! Send your answers, along with this form to: Talent Search, Dept. of Mathematics, NDSU, Fargo, ND 58105. Your Name: __________________________________     Set: 1 Your Address: __________________________________ 1. _____ __________________________________ 2. _____ __________________________________ 3. _____ Your High School: __________________________________ 4. _____ Grade: _____ Total: _____