PROBLEMS

  1. A square of side 2n inches long has two units squares removed from diagonally opposite corners. Can the remaining figure be covered by 2x1 non overlapping rectangles
  2. Prove that every right angled triangle with sides of integral length must have the length of one of its sides a multiple of 5.
  3. Two beakers have an equal amount of water and milk, one containing all water, the other all milk. A teaspoonful of milk is added to the water from the first beaker and then stirred. Then a teaspoonful of the mixture is transferred back to the first??(second) beaker. Is there more water in the milk or more milk in the water? What happens if the mixture is not stirred?
  4. A man has 12 billiard balls and a pair of scales. All balls look identical but one has a different weight to the others. Find this ball with a minimum number of weighings
  5. Five sailors are skipped on a desert island . The spend all day collecting coconuts which they put into a large pile. When they are asleep one awakes and decides to take his share i.e., one fifth. Unfortunately there is monkey watching so he tosses one to the monkey and then finds the pile divides evenly for his fifth. he takes his share and hides it. Each sailor then does exactly the same (including one to the monkey). What is the minimum number of coconuts needed so this can be done?
  6. Which is larger epi or pie? How would you prove this?