A homicide team enters a crime scene where a dead body of a fat old man lies there on the floor with blood oozing out of his head. The victim is holding a gun and a tape recorder lies there by his side. One of the detective picks up the recorder and plays it "I am tired of this life and hence I have decided to relieve myself from the worldly pains". A gunshot follows the message.
The teams starts investigating a murder investigation.
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
All Digits [0-9] follow the following pattern: There is one occurrence of all digits in every 10 numbers Example. Digit-9 occurred one time between 10 and 19 in 9, between 20 and 29 in 29
However, for tens(91,92,93...99) and hundreds (900,901.... 999), the occurrence is much more. Since we have included 1000, Therefor 1 is the most occurred digit.
Note: Despite three '0s' in 1000, 0 is not most occurred digit as they don't have tens and hundreds like other digits.
Two brothers have developed differences among themselves and thus want to part ways. The problem is that they have one big land that is irregular in shape. Both of them want an equal share which is fairly impossible as there is no way that land could be divided in equal halves due to irregularity in the shape.
The wisest man of the village is called who tells a way in which both of them will be happy even though the land might not be divided into exactly equal halves.
He simply suggested that one of the brothers will be allowed to divide the land but he must take into consideration that it will be the other one who will have a choice of selecting his land between the two halves first.
100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left.
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.
Imagine a picture in your mind. There is a rose plant. A few roses have grown up in the plant. There are a few bees hovering over them.
Now read the given statements carefully:
1) If every one of the bees lands on a rose, one of them won't get a rose.
2) If two bees share rise together, then there will be one rose left without any bee.
Can you find out the number of roses on the plant and the number of bees?
* They have only one torch and the river is too risky to cross without the torch.
* If all people cross simultaneously then torch light wont be sufficient.
* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.
What is the shortest time needed for all four of them to cross the river ?
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.
Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.
1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)
Alan is an honest person who never speaks a lie. He thinks of a number among 1, 2 and 3. Now, you can ask him only one question and that too for which the answer that you will receive will be in the form of yes, no or don't know. But he will reply only truth fully.
What will you ask from his so that you can know the number he is thinking of?