Three brothers share a family sport:
A non-stop marathon
The oldest one is fat and short
And trudges slowly on
The middle brother's tall and slim
And keeps a steady pace
The youngest runs just like the wind,
Speeding through the race
He's young in years, we let him run,
The other brothers say
'Cause though he's surely number one,
He's second, in a way.
You are sitting in front of your interviewer. He gives you three envelopes. One of them contains an offer letter and the other two are empty. You pick up one of them. Now, the interviewer opens up one of the envelope lying on the table and you find out that it is blank.
Now, he gives you a chance to switch your envelope with the one on the table. Would you switch it? Why or why not?
Yes, you should switch the envelope. In the beginning when you picked up the envelope, you had a 1/3 probability of finding an offer letter in the envelope. There was 2/3 chance that the letter was there in the two envelopes on the table.
If you keep your selected envelope, you still have a 1/3 chance of finding an offer letter in that. However, since the interviewer has removed one empty envelope from the table, if you switch, you have a probability of 2/3 that the offer letter is inside that.
A confectionary shop owner allows children to purchase a chocolate in exchange of five wrappers of the same chocolate. Children from the locality consumed 77 chocolates in a month. Now, they all collected them together and decide to buy back chocolates.
How many chocolates do you think they can buy using those 77 wrappers ?
The children can purchase 19 chocolates in return.
Out of 77 wrappers, 75 will be used to buy 15 chocolates and two will be left spare.
The 15 chocolates will create 15 empty wrappers that can be exchanged to get three chocolates.
Three chocolates will return three wrappers which will help them buy another chocolate.
Now the wrapper from this chocolate and the two spare that were left earlier will get them another chocolate.
15 + 3 + 1 = 19
There is no reason whatever why the customer's original deposit of Rs.100 should equal the total of the balances left after each withdrawal.
The total of withdrawals in the left-hand colum may equal Rs.100, but is is purely coincidence that the total of the right-hand column is close to Rs.100.
Let us show another example, but starting with Rs.200 in the bank:
Withdrawals Balance left
Moral of this story? Don't Total Balances
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).
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 are in a strange place which is guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there.
What should you ask?
If you ask the guard who always tells the truth, he would tell you the other guard would point you to the door of death. If you ask the guard who always lies, he would tell you the opposite door of the truth-telling guard and point you to the door of death. In either case, both guards will point to the door of death so you should choose the other one.
Two mathematicians Steven and James were sitting face to face when Steven came up with an idea in mind. He scribbled something on the table and told James to read it. James said that it was wrong. Steven said it is absolutely right.
What would Steven have scribbled to make both of them correct?
The number of decks is absolutely not relevant here which means whether we mix 5 or 500 cards still results would be same.
Any card drawn will be a Ace,2,3,4,5,6,7,8,9,10,Jack,Queen or King, so there are 13 possibilities each time a card is drawn.
If you are lucky just 5 cards of the same kind can be obtained in 4 steps
The unluckiest(worst) way is our solution as we need to guarantee a four of a kind.
Draw 3 of each kind =>now we have 39 cards. Next card will guarantee 4 of a kind.
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