## Thursday, June 21, 2007

### Microsoft Puzzles

The answers/hints of the puzzles are as follows:

1. HINT. The color of the bear is trivial. The possible solutions to it are interesting. In addition to the trivial north pole, there are additional circles near south pole. Think it out.
2. HINT. Join the centers of the original and the removed rectangle. It works for cuboids too! BTW, I have been getting many questions asking why a horizontal slice across the middle will not do. Please note the "any size or orientation" in the question! Don't get boxed in by the way you cut your birthday cake :) Think out of the box.
3. 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.
4. ANS. Divide the balls in three groups: 3 3 2

Now put first three at one side of balance and second 3 at another side of balance now there can be two possible cases:

CASE 1) Either the two balance will weight same.

If the two balance are weighing same the lesser weight ball must be in the 3rd group that is the group which is having two balls so now in remaining two balls we can identify which one is of less weight by one more weighing. (total of two weighing)

CASE 2) one of them will weight lesser.

The lesser weight ball must be in the group which is weighing less in the balance, now this group is having 3 balls, separate these 3 balls and put any of two on the balance now there can we two subcases:

Subcase 1: Either the two balance will weight same.In this case the remaining 3rd ball is of lesser weight.

subcase 2: one of them will weight lesser. This ball will be lesser in weight.

So in any possibility we have seen that we found the ball in two weighing.
two balls so now in remaining two balls we can identify which one is of less weight by one more weighing. (total of two weighing)
5. 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.
6. ANS: There could be many answers to this question:
* "There are 143,781,202 cars in the USA, if you disagree then count them all so you're sure I'm wrong."
* Population = 250 million
People per household = 3
Cars/household = 1
Avg life of car = 10 years

Total cars = ((25 X 10^6) / 3) / 10 - 1

* Total number of cars in the USA = (Total number of cars manufactured in the USA +

Total number of cars imported in the USA - Total number of cars exported from the USA)