PROBLEMS
- 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
- Prove that every right angled triangle with sides of integral length
must have the length of one of its sides a multiple of 5.
- 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?
- 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
- 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?
- Which is larger epi or pie? How would you prove this?