Puzzles for you

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OurKarnataka.Com introduces this section as a challenge as well as a learning channel for the visitors. The puzzles will be analytical or lateral thinking puzzles. We will also publish interesting facts, articles and trivia in this section. Send your answers, comments or interesting puzzles here.

At this point of time, we are giving you the answers straight away, since we haven't got anyone who took the challenge and solved it!
Thanks for the contributors who provide us with the puzzles and of course, the answers!!

Puzzles Edition 7
by Sridhar MV - San Jose, CA
Date Updated: 14 May 2003

Simple ones first!

Simple Puzzle1#
How many minutes after 3:00 PM or AM, will the 2 hands (hour hand and minute hand) be perpendicular again?
Click here to send your answers.. or click here to check if your answer is correct..

Simple puzzle 2# 
In a day, how many times will the hour hand and minutes hand cross over each other?
Click here to send your answers.. or click here to check if your answer is correct..

A really tough one now! Puzzle (really interesting!)

#Given that there are N number of people who do not trust each other, how can they divide an apple among themselves using a knife? Hint : If there are only 2 people, it is simple. One will make a cut to divide the apple into 2 pieces and the other will choose his piece first so both are happy. (they are happy because both cannot complain about this arrangement - if the first guy says he got a raw deal, it is his mistake that he cut unequal portions. He must have made a perfect cut when he had his chance. The second guy has nothing to crib anyway)

The solution to this problem for N > 2 will not be published and readers can send in their answers by Clicking here to send your answers. The correct answers along with the names of submitters will be published later.

Puzzle 6:  12 Identical Coins..
Problem : There are 12 identical coins (in look and weight). Only one of them is either slightly heavy or light. We have a scale that has two pans and we are allowed 3 trials to find the odd one and also tell if it is heavy or light. How would you do it ?  Click here to send your answers.. or click here to check if your answer is correct..
Puzzle Sent by Sridhar MV.

Tower of Hanoi!

No.. this has nothing to do with Vietnam!! This is an arithmetic puzzle thanx to someone named M. Claus (I don't have too many details about him) sometime in 1883.

"There are 3 (three) pegs fastened to a stand, consisting of eight circular discs of wood, each of which has a hole in the middle of through which a peg can be passed. Each of the discs have different radius. Initially, all the pegs are placed in one peg in such a way that the biggest one is in the bottom and smallest one is in the top. (This is where we get the name "Tower"!).

The puzzle is to shift the discs from one peg to another such that a disc will never rest on one size smaller than itself and finally move all the discs from the original peg to another peg so that they are back as a "Tower"!!!"

Answer: It takes about 18446744073709551615 separate transfers of each disc to achieve the above. And no.. I didn't do this calculation! Mr. Clause had enough time to do it for us and tell us the answer!!

Puzzle 5:  Heaven or Hell ?

Once a man die and went to the court of Chitragupt assistant of Yamaraja. Chitragupt looked into the man's life and found that he had done equal number of "punyas" (good deeds) and "papas" (sins). So he left the choice to the man himself but with one condition. The condition was as follows :

"There are two doors. One is to "swarga" (heaven) and the other to
"naraka" (hell). But you dont know which one leads to heaven and which one to hell. And there are two "dwarapalakas"(gatekeepers) among whom one always lies and the other always speaks truth. But you dont who is who?. Moreover you dont know at which gate they are standing. You have to ask only one question. It is left to you to choose whom to ask".

The man asked that single question to one of the gatekeepers and found the exact door to heaven. Now what would that question be if you ask will you know which gate is for heaven and which one is for hell?.

Answer

No one, has been able to produce a map that would need more than 4 colors!. But, at the same time, no one has been able to prove that all maps can be colored with only four colors!!

Nevertheless,   it is now known that if a map could be drawn which would require five colors, then there should be at least 36 countries
on it. Some one has also proved that with five colors you can cover any kind of map, but all five may not be necessary!!

Hmmmmmmm... interesting!

How did the word "Calculate" originate ?
When people first started to count, they slowly found out how to add, subtract, multiply and divide (probably in that order!). There came some special devices to make computation easier, especially when dealing with large numbers (like adding 6 and 16.. just kidding :-) 

The Romans used a counting frame, which is now known as "Abacus", using which units, fives, ten and so on were represented by beads which could be moved in groves. These beads were called "Calculi" which is plural for "Calculus". Since "Calc" means lime and marble is a kind of lime-stone, we can conclude that these beads were made of marble. 

What on earth is "Ahmes Rhynd Papyrus" ??
It is supposed to be the oldest mathematical book, written in 1550B.C. (of course, approximately!) 

Puzzle 4:  Who owns the Zebra?
Try to solve this puzzle...It's definitely solvable! The trick is HOW?
If you look at the problem mathematically, no sweat. If you get lost in the English, you are a dead meat. You will know you are right by checking the answer with all the conditions. This test was given by the German Institute of Logical Thinking in Berlin, 1981. ok, lets get started. Here is the puzzle and we hope you like it. Good luck...

There are five houses.
Each house has its own unique color.
All house owners are of different nationalities.
They all have different pets.
They all drink different drinks.
They all smoke different cigarettes.

The English man lives in the Red House.
The Swede has a Dog.
The Dane drinks Tea.
The Green house is on the left side of the white house.
In the Green house they drink coffee.
The man who smokes Pall Mall has birds.
In the yellow house they smoke Dunhill.
In the middle house they drink Milk.

The Norwegian Lives in the first house.
The man who smokes Blend, lives in the house next to the house with cats.
In the house next to the house with the horse, they smoke Dunhill.
The man who smokes Blue Master drinks beer.
The German smokes Prince.
The Norwegian lives next to the Blue House.
They drink water in the house that lays next to the House where they smoke Blend.

Who owns the Zebra?

would have covered 3 steps. By the time the faster guy reaches the floor, he would have covered 90 steps and our  slower pal covers 60 steps before he hits the floor.

Now the question is : how many steps are there on the escalator that can be seen from outside?

Note : no preference for the answers reached using equations. Logical reasoning is given preference.

Question :Now which one is more impure?

Hint: Again, Solutions reached using mathematics are not given preference.

There is this factory that makes pencils with the brand name as "PENCIL".   The brand name is printed on each pencil that the factory produces.  One fine day this printing machine goes nuts and starts printing the letters in random order. But it still prints only those 6 letters. For example, instead of "PENCIL" being printed on the pencils, we may find "NEPLIC" , "PLICEN" or any combination of those six letters.

Now, the question is, what is the probability that the letter L will come after I ?

Hint: You don't necessarily need to know probability theory or mathematics to solve this.. though it might help!

The man goes to one of the gatekeepers (it does not matter which gatekeeper) say GateKeeper_1 and asks him "If I go and ask the other gatekeeper (GateKeeper_2) 'WHICH IS THE GATE TO HEAVEN?' which gate would he show?". 

The man went to exactly the opposite gate indicated by the gatekeeper (GateKeeper_1).

EXPLAINATION :

Even the answer needs a bit of reasoning. Let us define some terms for reasoning. Let the gatekeepers be GateKeeper_1 and GateKeeper_2. You dont know who speaks truth always and who lies always. For simplicity let us consider two separate cases :
Suppose the man went to GateKeeper1 and asked the above question. There are two cases now :

CASE 1: Suppose the GateKeeper_1 always lies and GateKeeper_2 always speaks truth. Since GateKeeper_2 showed the correct gate (as he always speaks truth) to heaven GateKeeper_1 would lie (as he always lies) to the man that GateKeeper_2 would show the incorrect gate. So the man chooses the opposite one.

CASE 2: Suppose the GateKeeper_1 always speaks truth and GateKeepr_2 always lies. Since GateKeeper_2 showed the incorrect gate GateKeeper_1 would tell the man the truth that GateKeeper_2 would have shown had this man asked him.

Therefore in either case the man would choose the opposite gate shown by GateKeeper_1. This can be thought as AND logic in Digital Circuit Theory in Computer Science. Please spend some time in sketching some drawings and discover the answer.

If you need some more explanation please mail me.

Prashanth Beejadi 

Rajesh Virupaksha Munavalli

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