The CocoNut Problem

Five sailors survive a shipwreck and swim to a tiny island where there is nothing but a coconut tree and a monkey. The sailors gather all the coconuts and put them in a big pile under the tree. Exhausted, they agree to go to wait until the next morning to divide up the coconuts.

At one o'clock in the morning, the first sailor wakes up. He realizes that he can't trust the others, and decides to take his share now. He divides the coconuts into five equal piles, but there is one coconut left over. He gives that coconut to the monkey, hides his coconuts (one of the five piles), and puts the rest of the coconuts (the other four piles) back under the tree.

At two o'clock, the second sailor wakes up. Not realizing that the first sailor has already taken his share, he too divides the coconuts up into five piles, leaving one coconut over which he gives to the monkey. He then hides his share (one of the five piles), and puts the remainder (the other four piles) back under the tree. At three, four, and five o'clock in the morning, the third, fourth, and fifth sailors each wake up and carry out the same actions. In the morning, all the sailors wake up, and try to look innocent. No one makes a remark about the diminished pile of coconuts, and no one decides to be honest and admit that they've already taken their share. Instead, they divide the pile up into five piles, for the sixth time, and find that there is yet again one coconut left over, which they give to the monkey.

The Question: What is the smallest amount of coconuts that there could have been in the original pile?

You can also generalize the answer for n number of sailors by devising a C++ program.

Once Again, the Same Puzzle

Find the number of integral solutions to the following equation.
1/x + 1/y = 1/12

The Tourist : Lateral Thinking Puzzle

this is one of the standard L.T. puzzles: Enjoy!!!
the tourist from spain used to suffer from stomach pains regularly. Years ago his doctor had been born in goa. When he came back to his hotel, what was the landlady from israel watching on TV?

Level: Medium


I have a nice clue....request in comments if wanted.

Möbius strip

A Möbius strip is a surface with one and only one side. You might have seen a ring which has two distinct sides, one outside and one inside, but, as you see, the inside merges into the outside and the outside into inside in a Möbius strip. A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a single strip. The strip was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.

The Möbius strip is a peculiar object and has curious properties like:





(i) A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip of paper. This single continuous curve demonstrates that the Möbius strip has only one boundary.

(ii) If the strip is cut along the above line, instead of getting two separate strips, it becomes one long strip with two full twists in it, which is not a Möbius strip. This happens because the original strip only has one edge which is twice as long as the original strip of paper. Cutting creates a second independent edge, half of which was on each side of the knife or scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other.

The branch of Mathematics dealing with such objects is called Topology. Another such mysterious object is the Klein bottle, depicted on the left. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. The Klein bottle has no distinct outside or inside and has no edges.

The Comparision of The TITANS

Have a look at this greatest comparision between the 2 most popular teams in the world





An Effort By:

Sajal Jain
Shikhar Srivastav

First Puzzle : The Monkey Dance

Ok friends, Hi I am Mayank Gupta......Thanks first of all to Sajal for inviting me to this blog....he must have surely been in a state of hypnotism when he sent an invite to a dunce like me.......

So I start with one of my favourite puzzles....well it came in ZIO 2005:
The director of Hind Circus has decided to add a new performance called the monkey
dance to his show. The monkey dance is danced simultaneously by N monkeys.
There are N circles drawn on the ground. There are N arrows drawn between the
circles in such a way that for each circle, exactly one arrow begins at that circle and
exactly one arrow ends at that circle. No arrow can both begin and end at the same
circle.
When the show begins, each monkey sits on a different circle. At each whistle of the
ringmaster, all the monkeys simultaneously jump from one circle to the next, following
the arrow leading out of the current circle. This is one step of the dance. The dance
ends when all the monkeys have simultaneously returned to the circles where they
initially started.
The director wishes the dance to last as many steps as possible. This can be achieved
by drawing the arrows intelligently.
For each of the three values of N given below, what is the maximum number of steps
that the monkey dance can be made to last by drawing arrows appropriately?

(a) 9 (b) 12 (c) 15

Sajal: Don't ans since u already know the soln.

Level : Difficult

Weigh It

Suppose five bales of hay are weighed two at a time in all possible ways. The weights in pounds are 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121.

How much does each bale weigh?

Level:Medium

Flowers

In a small town, there are three temples in a row and a well in front of each temple. A pilgrim came to the town with certain number of flowers.

Before entering the first temple, he washed all the flowers he had with the water of well. To his surprise, flowers doubled. He offered few flowers to the God in the first temple and moved to the second temple. Here also, before entering the temple he washed the remaining flowers with the water of well. And again his flowers doubled. He offered few flowers to the God in second temple and moved to the third temple. Here also, his flowers doubled after washing them with water. He offered few flowers to the God in third temple.

There were no flowers left when pilgrim came out of third temple and he offered same number of flowers to the God in all three temples. What is the minimum number of flowers the pilgrim had initially? How many flower did he offer to each God?

Level:Easy

River Game!

THE AIM

The object is to get everyone (father, two sons, mother, two daughters, police officer and thief) from one side of the river to the other whilst adhering to certain rules.

THE RULES
The following rules apply:

1. Only two persons on the raft at any time
2. The father can not stay with any of the daughters without their mother's presence
3. The mother can not stay with any of the sons without their father's presence
4. The thief (striped shirt) can not stay with any family member if the police officer is not there
5. Only the father, the mother and the police officer know how to operate the raft

Some of the classics of KVPY

1) How many 4 digit square numbers exist such that after increasing each digit by 1 we get another square number?
2)3 points lie in the x-y plane such that coordinates are (0,0),(6,0),(2^1/2,3).Find the largest side of the square inscribed in it such that the 2 vertices's of square lie on AB(x-axis).
3)A circuit diagram is drawn with 1 ohm resistance lying along the sides of a cube and a 10v battery is connected to it. Find the current in the circuit.
4)A light ray is sent from vertex A of a square making an angle "theta" with the side AB. The ray after being reflected from side BC,CD,DA passes through vertex B. Find sin"theta".

To Shikhar and Ananth,
Anybody solving all 4 correctly deserves a treat from me.

If you have any confusion regarding any question please comment.

One of the Classics

The King of Honolulu tells his two sons to race their ships to a distant city to see who will inherit his fortune. The one whose ship is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advice. After hearing the advice they jump on the ships and race as fast as they can to the city.
What does the wise man say?

This is one of the classical puzzles and very old. So may be you done this already.