1. Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife?

ANS. Join the centers of the original and the removed rectangle. It works for cuboids too!

2. There are 3 baskets. one of them have apples, one has oranges only and the other has mixture of apples and oranges. The labels on their baskets always lie. (i.e. if the label says oranges, you are sure that it doesn’t have oranges only,it could be a mixture) The task is to pick one basket and pick only one fruit from it and then correctly label all the three baskets.

HINT. There are only two combinations of distributions in which ALL the baskets have wrong labels. By picking a fruit from the one labeled MIXTURE, it is possible to tell what the other two baskets have.

3. You have 8 balls. One of them is defective and weighs less than others. You have a balance to measure balls against each other. In 2 weighings how do you find the defective one?

Answer from Uday Venkat: weigh three balls against another three balls. if both weigh the same , then just weighing the remain two (one against one) will show the lighter ball. if the sets of three do not weigh equal, then weigh any two balls in the lighter set, one against the other . the balance will show if the lighter one is on the balance,if not the remaining one is the lighter one.

8= (3 + 3 ) + 2

(the numbers in the brackets are balls on either side of the balance)

if both are equal, then

2= (1 + 1) done.

else, from the lighter set of 3

3= (1 + 1) + 1 done.

4. Why is a manhole cover round?** **

HINT. The diagonal of a square hole is larger than the side of a cover!

Alternate answers: 1. Round covers can be transported by one person, because they can be rolled on their edge. 2. A round cover doesn’t need to be rotated to fit over a hole.