Mind Benders Puzzles

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.

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.

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.

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.

54
7^2 + 2^2 + 1^1
6^2 + 3^2 + 3^2
2^2 + 5^2 + 5^2

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.

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.

He was Mass Murderer.

Density multiplied by volume equals mass.
Therefore, Luis Garavito killing mass would mean Luis Garavito was a MASS murderer

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.

It lasted from 1337 to 1453 i.e. 116 years.