What was the duration for which the hundred years war lasted ?
It lasted from 1337 to 1453 i.e. 116 years.
A convention is held where all the big logicians are summoned. The master places a band on everyone’s forehead. Now all of them can see others’ bands but can’t see his own. Then they are told that there are different colors of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the color of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.
The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?
First the logicians will have to take a leap of logic. The master has told them that it won’t be impossible for any logician to solve the puzzle. Thus it is assure that any of the color can’t exist only once. If it did, the one wearing it will have no clue about that color which would be unfair for him.
Now every logician will look around in the circle and count the number of times they see a particular color. If a color is seen only once, then the logician will know that the color on his band must be of the same color (as per the leap of logic). And then the logician will leave on the first bell.
In the similar fashion, any logician who see any color just once will be able to identify his own color and they will leave when the bell rings or they will be disqualified and asked to leave. Equivalently, any color for which there are two bands, will be eliminated after the first bell has rung. Thus there must be three bands of any remaining color at least.
Assume that a logician don’t see any color once, but sees a color twice. If they were the only bands of this color then the two logicians must have left at the first bell. But they did not. Thus it means that his band color is the same and he will leave on the second bell.
The wisest men of the kingdom are called upon by the king to his court. One of them is to be chose for the advisor rank and thus they shall prove their worth in the test. The king places hat on each of their hats. Each one of them can see other two hats but can't see his own. The hats are either white or black.
For a hint, the king tells them that at least one of them is wearing a black hat. Also the king declares that the test is totally fair for each one of them. Now the first one from them who is able to deduce the color of hat he is wearing will be designated as the advisor. After a few minutes, one of them was able to deduce the color of his own hat. How ?
Suppose that there is just one black hat. In such a scenario, the person wearing it will see the other two hats as white and then as the king had announced, he will be easily able to judge that he is wearing a black hat himself. But the other two men will see a black hat and a white hat and will not be able to judge. Thus this will be an unfair situation, so we can rule it out.
Now suppose that there are two black hats. Then, both the person will see a white hat and a black hat. And they have already realized that there must be two black hats, thus they can easily deduce that they are also wearing a black hat. But the one wearing white hat will see two black hats and thus he will not be able to identify on a sure note. Thus the competition will not be fair.
Thus the only situation where the competition can be fair is when all the hats are black. The first one who recognize the fact will stand up and say black.
During an experiment, a guy throws a bouncy ball from a 90 feet tall building. The ball has a specific characteristic. Every time it hits the ground, it bounces up half way.
How many bounces do you think the ball will make before it comes to a stop ?
Clearly as per the data given in the question, the ball will always keep on bouncing half way up and thus it will take infinite bounces before the gravity forces it to stop.
There are two bottles that consists of different pills each. You must take the two pills at the same time and if you forget, or just take one of them or take two of the same kind, you will die a miserable death. In a hurry, you pour from both the bottles at the same time and three pills fall down in your hand.
Now you can’t throw away the pills as they are quite rare to be found. Also both of the pills look exactly the same and have all the characteristics similar. How will you ensure that you don’t take a wrong pill and die ?
All you have to do is labelling the pills as A and B. Now when you draw out three pills, you will either have 3A or 2A 1B or 1A 2B or 3B. Now if all the pills are from same bottle you can simply take another from the other bottle. If some other combination comes out, you can manage by filling in from the required bottles.
Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.
On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?
Friend 2 must have taken top 15 cards from the pile and reversed them. Now there are two piles, one with 15 cards and one with 37 cards and both of them will obviously have the same number of inverted cards.
If you want to understand mathematically, let us say that there were x inverted cards in the top 15 cards of the deck. Then the remaining 37 cards will comprise of 15-x number of inverted cards.
If we reverse the 15 cards the number of inverted cards will become 15-x and the number of inverted cards will be same in both the piles.
If an earthquake is 1 point higher on the Richter Scale than another earthquake which is actually 10 times stronger, how much stronger would an earthquake be if it was just half a point higher on the Richter scale?
The most common answer would be 5. But that’s totally incorrect. It will be the square root of 10 times stronger i.e. 3.16 times.
A dying old man wants to divide his entire land between his only two sons. Since his only wish is to treat them as equal as both of them have been too good to him, he wants to divide his land equally between them. The problem is that the land is significantly irregular in shape and thus there is no choice of cutting them in two equal halves.
Can you help him divide the land in a manner that both of his sons will be happy ?
All he need to do is ask one of his son to divide the land in two part and tell him that the other son will have the choice of selecting one of those two halves.
In this manner both of them will be happy.