24 times is the most common answer however that is completely wrong. The right answer will be 22 times.
Let us prove it by some simple mathematics.
Assume that it takes T hours for the minute hand to complete T laps. The hour hand will complete T/12 Laps in the same time.
Consider the situation when the hour hand and the minute hand will overlap for the first time; the minute hand would have completed one lap extra than the hour hands.
Thus, T =T/12 + 1
Considering the above expression we know that the first overlap will take place after t = 12/11 hours i.e. 1:05 am.
Similarly, the second overlap will take place when the minute hand would have completed two more laps than the hour hand.
Considering there are X laps,
T = T/12 + X
Everyone knows that a day comprises of 24 hours. Putting that in the equation we get
24 = 24/12 + X
Solve it and you will get
X = 22
Hence both of the hands will overlap 22 times in 24 hours.
Let us give you with those exact timings as well.
The hands will overlap at 12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45, and 10:50. Do consider the fact that there will be no 11:55. It becomes 12:00.
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?
In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?
The answer is 2. First, divide the coins into 3 equal piles. Place a pile on each side of the scale, leaving the remaining pile of 3 coins off the scale. If the scale does not tip, you know that the 6 coins on the scale are legitimate, and the counterfeit is in the pile in front of you. If the scale does tip, you know the counterfeit is in the pile on the side of the scale that raised up. Either way, put the 6 legitimate coins aside. Having only 3 coins left, put a coin on each side of the scale, leaving the third in front of you. The same process of elimination will find the counterfeit coin.
For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 276 books with me to gift her.
Can you calculate, on which day is our anniversary?
There are 100 doors. 100 strangers have been gathered in the adjacent room. The first one goes and opens every door. The second one goes and shuts down all the even numbered doors – second, fourth, sixth... and so on. The third one goes and reverses the current position of every third door (third, sixth, ninth… and so on.) i.e. if the door is open, he shuts it and if the door is shut, he switches opens it. All the 100 strangers progresses in the similar fashion.
After the last person has done what he wanted, which doors will be left open and which ones will be shut at the end?
Think deeply about the door number 56, people will visit it for every divisor it has. So 56 has 1 & 56, 2 & 28, 4 & 14, 7 & 8. So on pass 1, the 1st person will open the door; pass 2, 2nd one will close it; pass 4, open; pass 7, close; pass 8, open; pass 14, close; pass 28, open; pass 56, close.
Thus we can say that the door will just end up back in its original state for each pair of divisor. But what about the cases in which the pair of divisor has analogous number for example door number 16? 16 has the divisors 1 & 16, 2 & 8, 4&4. But 4 is recurrent because 16 is a perfect square, so you will only visit door number 16, on pass 1, 2, 4, 8 and 16… leaving it open at the end. So only perfect square doors will remain open at the end.
You have ten boxes and an electronic weighing machine. In those ten boxes, you have chocolates. Each chocolate weigh 20 grams. But in one box the chocolates are defective and each weigh 19 grams exactly.
Now you can weigh in the electronic weighing machine but you can use that machine just once. How will you find out which box has the defected chocolates.
If you are thinking to hold one chocolate from each box in hand and then balancing weight in bare hands, you are thinking all wrong.
Let us begin by labelling boxes as 1, 2, 3 and so on till 10.
Now pick one chocolate from box 1, two chocolates from box 2, three from box 3 and so on. In total, you will have 55 chocolates now. (1 + 2 + 3 + ..... + 10)
The ideal weight of the chocolates should be 55 * 20 = 1100. However, somewhere in there are the defected chocolate/s.
You can judge that clearly by noting down the result of 1100 - total weight of chocolates. If the weight is less than 1 gram, the defected box is box 1, if the weight is less than 2 grams, the defected box is box 2 and so on.
The toothpicks in the picture have been arranged to form a donkey shaped figure. You have to move two matchsticks in a way that the entire shape is rotated / reflected while being intact. Also, you can't change the tail's direction it should be pointing up.
They have property such that when you light the fire from one end , it will take exactly 60 seconds to get completely burn.
However they do not burn at consistent speed (i.e it might be possible that 40 percent burn in 55 seconds and next 60 percent can burn in 10 seconds).
Before going to work, Inspector Montalbano got into the fight with his wife. After coming back from the work he found out that the police was in the home and his wife had just killed a burglar.
The police told that she killed the burglar in self-defense. She told her husband the story that she heard a doorbell and thought that it was me and as soon as she opened the door, the burglar jumped into her and she was so scared that she killed burglar immediately with the knife. Inspector Montalbano asked the police to arrest her wife for murder conspiracy. Why?