Interactive Mathematics Miscellany and Puzzles is a frequently updated site. Here are the most recent addtions. For other changes please visit the site. Optimization in a Crooked Trapezoid. One of the sides of a trapezoid is a circular arc. Maximize the area of the trapezoids cut off by the tangents to the arc http://www.cut-the-knot.org/Optimization/CrookedTrapezoid.shtml Huygens' Problem. Given a straight line lambda and points C and D on the same side from lambda. Find on lambda point P that minimizes CP^{2}+DP^{2} http://www.cut-the-knot.org/Optimization/Huygens.shtml Distance Between Projections. Minimize the sum of distances from a point to a given set of points, all on the same straight line http://www.cut-the-knot.org/Optimization/DistanceBetweenProjections.shtml Residence at an Optimal Distance. Minimize the sum of distances from a point to a given set of points, all on the same straight line http://www.cut-the-knot.org/Optimization/OptimalResidence.shtml Three Checker Game on a One Row Board http://www.mathteacherctk.com/blog/2012/05/three-checker-game-on-a-one-row-board/ A Crooked Polygon http://www.mathteacherctk.com/blog/2012/05/a-crooked-polygon/ An even Better Butterfly Theorem: a generalization of the Better Butterfly theorem to two co-axial similar conics http://www.cut-the-knot.org/pythagoras/ButterflyInConics.shtml Engaging Math Activities for the Summer Break http://www.mathteacherctk.com/blog/2012/05/engaging-math-activities-for-the-summer-break/ Parity Games http://www.mathteacherctk.com/blog/2012/05/parity-games/ X and the City - a Review http://www.mathteacherctk.com/blog/2012/05/x-and-the-city-a-review/