A couple had to take shelter in a hotel for they could not proceed their journey in the rain. Having nothing to do at all, they started playing cards. Suddenly there was a short circuit and the lights went off. The husband inverted the position of 15 cards in the deck (52 cards normal deck) and shuffled the deck.
Now he asked his wife to divide the deck into two different piles which may not be equal but both of them should have equal number of cards facing up. There was no source of light in the room and the wife was unable to see the cards.
For a certain amount of time, she thought and then divided the cards in two piles. To the husband’s astonishment, both of the piles had equal number of cards facing up.
The answer is very simple. All she had to do is take the fifteen cards from the top and reverse them. This would make another pile out of that and there will be two piles - one of 15 cards and one of 37 cards. Also both of them will have the same number of inverted cards.
Just think about it and if the mathematical explanation will help you understand better, here it is.
Assume that there were p inverted cards initially in the top 15 cards. Then the remaining 37 cards will hold 15-p inverted cards.
Now when she reverses the 15 cards on the top, the number of inverted cards will become 15-p and thus the number of inverted cards in both of the piles will become same.
For each 5 miles driven using this rotation, each tire will lose (2/29000)+(2/21000) of its tread.So, suppose we drive 5*N miles like this. Then, each tire will lose 2*N*((1/29000)+(1/21000)) of its tread. We wish to determine N so that the latter expression gets to be 1, representing all of each tire's tread. That happens when N=6090, which is when 5*N (the total miles driven) is 30,450.
There are three cars in a racing track. The track is made forming a perfect circle and is quite wide so that at one time, multiple cars can pass through it. The car which is leading is driving at 55 MPH and the slowest car is driving at 45 MPH. The car that is in middle of these two is driving in between the two speeds. For the time being you can say that the distance between the fastest car and the middle car is x miles and it is same between the middle car and the slowest car. Also, x is not equal to 0 or 1.
The car keeps running till the leading car catches up with the slowest car and then every car stops. Given the case, do you think that at any point, the distance between any two pairs will again become x miles?
In the question, the distance of x miles is given at a particular moment. The middle car is running at that time at 50 MPH. The distance will keep increasing with time as three are running at different speeds. It will increase by x miles every hour till a certain point of time and then it will start decreasing till the fastest car meets the slowest again.
As per question, all the cars stop then. Thus, the distance will never be x miles again.
We know that Christanio Ronaldo tells the truth on only a single day of the week. If the statement on day 1 is untrue, this means that he tells the truth on Monday or Tuesday. If the statement on day 3 is untrue, this means that he tells the truth on Wednesday or Friday. Since Christanio Ronaldo tells the truth on only one day, these statements cannot both be untrue. So, exactly one of these statements must be true, and the statement on day 2 must be untrue.
Assume that the statement on day 1 is true. Then the statement on day 3 must be untrue, from which follows that Christanio Ronaldo tells the truth on Wednesday or Friday. So, day 1 is a Wednesday or a Friday. Therefore, day 2 is a Thursday or a Saturday. However, this would imply that the statement on day 2 is true, which is impossible. From this we can conclude that the statement on day 1 must be untrue.
This means that Christanio Ronaldo told the truth on day 3 and that this day is a Monday or a Tuesday. So day 2 is a Sunday or a Monday. Because the statement on day 2 must be untrue, we can conclude that day 2 is a Monday.
So day 3 is a Tuesday. Therefore, the day on which Christanio Ronaldo tells the truth is Tuesday.
A guy claims to do the following thing. He puts a coin in a glass bottle. Then, he shuts the mouth of the bottle with the help of a cork. Now he manages to remove the coin out from the bottle without taking out the cork or breaking the glass bottle.
A thief was running from the police after the biggest theft the town saw. He took his guard in one of the thirteen caves arranged in a circle. Each day, the thief moves either to the adjacent cave or stay in the same cave. Two cops goes there daily and have enough time to enter any two of the caves out of them.
How will the cop make sure to catch the thief in minimum number of days and what are the minimum number of days?
A professor gives a set of three questions to the most brilliant students of his university. You can see the questions in the attached image if required. To his surprise, there are different answers by all three of them. Below are the answers by them:
Now you have the information that each one of them has given one answer wrong, can you find out the real answers to every problem?
Since each one of them gave one answer wrong, this means that each one of them gave two answers right.
Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.
Thus both Student A and Student B must be right with the first question and the answer to the first is two.
If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
You are stuck with the pirates who might even kill you on board. They give you a chance to survive. There are hundred black rocks and hundred red rocks. There are two empty sacks which are labelled as heads and tails respectively. You have to divide the rocks in two bags as per your wish. Then a fair coin will be flipped. If its heads, you will have to pick a rock on random from the sack labelled heads and if its tails, you will pick up from the tails sack. If you pick up a black rock, you will be freed and if you pick up a red rock, you will be killed.
How will you distribute the rocks so that your chances of survival are the best?