The master of logic.

Three masters of logic wanted to find out who was the wisest one. So they invited the grand master, who took them into a dark room and said: "I will paint each one of you a red or a blue dot on your forehead. When you walk out and you see at least one red point, raise your hands. The one who says what colour is the dot on his own forehead first, wins." Then he painted only red dots on every one. When they went out everybody had their hands up and after a while one of them said: "I have a red dot on my head."
How could he be so sure?

difficulty - easy - medium.

The Cauldron of Death

Once upon a time, there was a prisoner trapped in the Cauldron of Death. There were two doors to exit from, one leading to the hungry alligators and the other leading to the actual exit. There were two guards who were keeping vigil of the prisoner. The prisoner, a clever man, bribed them so that they would tell him which door to go through, but he could ask only one question to only one of the guards. One of the guards always lied while the other had never ever said a lie in his whole life - He didn't know which one. The prisoner managed to escape from the clutches of the alligators and the guards. How? What question do you think he asked one of the guards?

EQUATION

Fill in the eight missing digits so that the equation is correct and uses each of the digits from 0 to 9.(7 and 5 have already been used).

Leval:Medium

Time Warp

An event took exactly 131 seconds. The first picture of a 24-hour digital clock shows the time when the event began, the second one when it ended. However, there was a strange breakdown, and some parts of the display are not visible; the nature of the breakdown was different for the two times. What are the two times?
Note:Click on the picture to view it clearly.
Hint:The answer is unique.

Level:Medium

Hourglasses

You have two hourglasses: A 7 minute one and an 11 minute one. Using just these 2 hourglasses, accurately time 15 minutes.

A more wordy version of this - A baker has only 2 timers that can measure 7 minutes and 11 minutes. How can he set a timer for 15 minutes to bake a cookie?

Level:EASY

CJ (Chonkar Joke)

Master: Chicken ready ?
Servant: Yes sir
Master: Fish ?
Servant: Yes sir
Master: Mutton ready?
Servant: Yes sir
Master: Aur bakra
Servant: No sir, abhi voh blog par CJ padh raha hai.

Zonal Informatics Olympiad 2007

Zonal Informatics Olympiad coming up.
Its on 17th November 2007.
The questions are generally logical based puzzles.One of the questions of last year has been posted recently as "Weigh it!"
If you want to participate, please contact the undersigned:

Sajal Jain
XI G

Weigh It!

In a normal pan balance (as used by, say, a vegetable vendor) the item to be bought is balanced against a known combination of weights. The weights may be applied on either side of the pan--for instance, to weigh 1500 g of onions, the vendor may either place the onions in one pan and a 1000 g and 500 g weight in the other, or place the onions along with a 500 g weight in one pan and a 2000 g weight in the other pan.

We would like to be able to weigh all quantities between 1 g and 4000 g to the nearest gram using such a balance. One way to do this is to have 12 weights weighing 1 g, 2 g, 4 g, 8 g, 16 g,..., 2048 g.

1. Design a smaller set of weights to achieve the same objective.

2. In general, to weigh items between 1 g and n g to the nearest gram, what is the smallest sequence of weights we can use (in terms of n)?

Level:Medium-tough