Suppose that A, B, and C are the vertices of a triangle and P is any point inside the triangle. Show that AP + BP < AC + BC. Albert and Zeb recently went on a hunting trip. They left very early in the morning, and after driving for 30 miles, Albert decided he was getting sleepy and asked Zeb to drive while he took a nap. Now, Albert slept more than he planned, and woke up just a few miles from the place they were going to hunt. On the way back Albert offered to drive while Zeb read a book, but after a rest stop 60 miles out from Fargo, he was beat and Zeb took over the driving. If they took the same route on their way there as on their way back, how much more driving did Zeb do? In a standard game of Tic-Tac-Toe, how many ways are there to tie? In other words, how many different arrangements of X's and O's are there in which there are no three-in-a-row? Five points are randomly placed on the surface of an icosahedron (a regular solid with 20 faces). Show that there is a plane which divides the icosahedron in two pieces with equal volume and has at least 4 points on one side of it. (Hint: You may assume that points on the plane live on both sides of it.) With 100 members voting, the ND House of Representatives defeated a bill. A re-vote, with the same members voting, resulted in passage of the bill by twice the margin by which it was originally defeated. The number voting for the bill on the revote was 12/11 of the number voting against it originally. How many more members voted for the bill the second time than voted for it the first time? On the graph of y = x2 , how many pairs of points with integer coordinates are there that determine a line of slope 1? Previous Years: Talent Search 1998-1999 Talent Search 1999-2000 Talent Search 2000-2001 Talent Search 2001-2002 Talent Search 2002-2003 Talent Search 2003-2004 Talent Search 2004-2005 Talent Search 2005-2006 Talent Search 2006-2007 Talent Search 2007-2008 Talent Search 2008-2009