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Mathematics 

MathMania 2003 Problems

  1. A circle and a parabola are drawn in the plane. What is the largest number of regions they divide the plane into?
  2. From a group of boys and girls, 15 girls leave. There are then two boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. What was the number of girls originally present?
  3. What is the smallest positive integer x such that 750 x is a perfect square?
  4. At 2:15, what is the angle between the hour hand and the minute hand of a clock?
  5. The large square shown has area 1. The four interior lines each join a vertex of the square to the midpoint of a side as shown. What is the area of the small central square?  
Square ABCD is shown with points X,Y,Z, and W being the midpoints of sides AB,BC,CD, and DA, respectively. Segment AY meets segments BZ and DX in points P and Q respectively and segment CW meets segments BZ and DX in points S and R respectively. The square PQRS is formed.

 

 

 

Square ABCD is shown with points X,Y,Z, and W being the midpoints of sides AB,BC,CD, and DA, respectively. Segment AY meets segments BZ and DX in points P and Q respectively and segment CW meets segments BZ and DX in points S and R respectively. The square PQRS is formed.

  1. Solve the equation x2 + x - 8 = |x|.
  2. What is the number of digits in 20032003?

Here are the answers.