I. No Math Knowledge Required

• The floor of a square room needs to be tiled. The size of the floor is 8 m by 8 m. On diagonally opposite corners of the room, there stand two square pillars measuring 1 m by 1 m. The tiles are rectangular, 2 m long and 1 m wide. So the architect buys 31 such tiles to cover the floor. Now, can she tile this floor using these 31 tiles without having to break a tile into two? If Yes, how? If No, why not?
  Hint: Think CHESS BOARD!

• You are given two pieces of string made from a strange material, and a match box. You are told that the strings have been made in such a way that when lit from any one end, each string burns all the way in exactly 1 hour. The strings however, have been made by hand, so they don't burn evenly. So all you know is that the whole string will burn in an hour, not that half of it will burn in half-an-hour etc. Can you use the strings to measure 45 min?

II. A little Math Knowledge Required

• Given a triangle, suppose that the lengths of the angle bisectors of any two of its angles are equal. Prove that the triangle is isosceles.