Mind Teasers :
Classic Pigeonhole Principle Puzzle
You were hanging out in the New York City when a man in suit approached you. He said that he was ready to bet a hundred bucks to the fact that there are at least two people (excluding the bald people) in the City with same number of hairs.
Seeking the impossibility of the case, you thought of accepting the bet.
After the discussion of two minutes, you realized that you had lost the bet.
The total population of New York City is about nine millions. Let us assume that 1 million among them are bald which leaves us with eight millions of people that are required to have different number of hairs on their head.
Now as per the surveys, on an average, people have 100, 000 hairs on their head. Since all must have different numbers, we start with one. Let us say someone has one hair strand, someone has two, and someone has three and so on. After 100, 000 people, we are left with 7, 900, 000 people left. Since all of them are needed to have different number of hair strands, we will move up from 100, 000.
In such case, at the end, you will be having a person with 8, 000, 000 hairs which is clearly impossible (even having 1, 000, 000 hairs on someone's head is impossible).
Therefore, there must be two people who have same number of hairs on their head.
This is a classic example of the pigeonhole principle.
AS you can see the picture, all you have to do is analyze it and tell who all from the pictured people will die if the person at E pushes the round object to the slide on the slope. Keep in mind all the physics and the terrain while you analyze the things.
If you notice the animated gif, you know that D, C and B are going to die. D dies directly after coming in contact with the object, C dies after being thrust by the spikes of the see-saw and B dies with the blue ball.
But consider the situation that the person at E stands for Ebola. Eventually A dies as well.
Suppose there is a Christmas tree and four angels are sitting on it amidst the other ornaments. Two of them have black halos and two of them have white halos. No body among them can see above their head. Angel A is sitting on the top branch and can see angels B and C sitting below him. B can see C who is sitting in a branch lower than his. Angel D is at the base of the tree and can't be seen due to the branches in between. Also, he can't see anybody as well.
If they are asked to guess the color of their own halo (they dont know that), who do you think will be able to deduce and speak up first with a right answer?
Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.
So either A or B will speak up first depending on the situation.
As shown in picture, there are four gears with the following specification
* Gear A has 60 teeth
* Gear B has 40 teeth
* Gear C has 20 teeth
* Gear D has 60 teeth
* Every minute, Gear B makes 15 complete turns.
You have to place all the digits from 1 to 9 without repeating any number in a tic tac toe board. The condition is that the numbers should add up to 15 whether you add the numbers in each row, column or diagonally.
The three errors are as follows:
a) fynd is spelled wrong. The correct spelling is 'find'.
b) that is not appropriate to use here. It should be 'this'.
c) There are only two errors in the question and that is the third error because the questions asks us to find three.
In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly
It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.
An old man in the village feels that his end is near. He calls his two sons to discuss about the land he owns and other properties. He tells them to have a race on their horses till the city border. The one with the slower horse will be rewarded with the entire property.
Both of them keep wandering here or there without any result as no one is filling to reach the border. Then they visit the wise man of the village and seek his advice. The wise men tells them something listening to which they jump on the horses and race as fast as they can till the city border.
Step1. Lets say y = x
Step2. Multiply through by x xy = x2
Step3. Subtract y2 from each side xy - y2 = x2 - y2
Step4. Factor each side y(x-y) = (x+y)(x-y)
Step5. Divide both sides by (x-y) y = x+y
Step6. Divide both sides by y y/y = x/y + y/y
Step7. And so... 1 = x/y + 1
Step8. Since x=y, x/y = 1 1 = 1 + 1
Step9. And so... 1 = 2
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules
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