Adam was moving down in an elevator. The elevator stopped and the remorse on his face was clear.He knew Eve had died.
How did he know?
Eve was admitted in hospital was under life support system. Adam had just visited her and was moving down the elevator when it stopped suddenly. He knew it was the power cut and the backup generators were clearly not working or the elevator would have worked. Thus he assumed that even the life support system had stopped.
Alpha and Beta are playing bets. Alpha gives $10 to Beta and Beta deals four card out of a normal 52 card deck which are chose by him completely randomly. Beta keeps them facing down and take the first card and show it to Alpha. Alpha have a choice of either keeping it or to look at the second card. When the second card is shown to him, he again has the choice of keeping or looking at the third which is followed by the third card as well; only if he does not want the third card, he will have to keep the fourth card.
If the card that is being chosen by Alpha is n, Beta will give him . Then the cards will be shuffled and the game will be played again and again. Now you might think that it all depends on chance, but Alpha has come up with a strategy that will help him turn the favor in his odds.
Can you deduce the strategy of Alpha ?
To keep odds in his favor, Alpha must choose a card from the first three whenever he sees a 9 or higher card.
This is because the probability that all cards that are selected randomly by beta are below 9 is 32*231*30*29 / 52*51*50*49 = 0.133.
In such a case, you lose from $2 to $9 with equal probability = 0.133/8 = 0.0166
Let us now calculate the probability of the four cards being of value 9 or higher which will be equal to 1 – 0.133 = 0.867.
As Alpha stops at the first sight of 9 or a higher card, he can possibly win -1, 0, 1, 2, 3 with an equal probability of 0.867/5 = 0.173
This will give him an overall expected winning amount of 0.14 per game he plays.
Also note that if Alpha decides to stop at a card 10 or higher, the expected winning amount will be 0.09 per game. It can be a strategy to win more but will not stand quite effective.
With any other choice of stopping, Alpha will be having negative chances of winning.
Indiana Jones has stolen two solid gold bars from a treasure. But now, the village people are behind him. While running away from them, he comes across a bridge formed by a single rope. Now he knows that he can cross the bridge on that rope. But there is a signboard which reads that the rope can carry a maximum weight of 130 pounds only.
Now, the gold bar weighs 20 pounds each and he weighs 100 pounds. How will he cross the bridge now given that he can't leave the gold bar behind and he don't have enough time to return back and take them one by one ?
If you know about the weighing systems, you must be knowing that gold is weighed in Troy system while otherwise normally, the weight is measured using the imperial system.
In Troy system, 12 ounces = 1 pound.
In imperial system, 16 ounces = 1 pound
Thus, 40 pounds of gold weighed in Troy system will be only 30 pounds in the imperial system of weighing. The weight limit for the rope must be in imperial system only as that is the standard weighing system.
Thus the total weight = 100 + 30 = 130 pounds and all he will do is simply walk it carrying both the gold bars.
A pocket watch is rotated voluntarily. See the picture given with this question. If the colored hands represents the hour, second and minute hands of the watch, can you determine the time? Hint: It's somewhere in the afternoon.
There are sixty marks, so logically each mark is there for a minute.
Now, the hour hand is on a mark when the minute hand is on [0, 12, 24, 36, 48]. When the minute hand is on a mark, the second hand is on noon. But the blue hand cannot be the second hand. (It would be on noonand it would be eighteen minutes past/before a full hour.)
a) Green is on twelve. Red indicates twenty four minutes. Blue indicates forty two [minutes] = 8 + 2/5 [hours] = 8:24
b) Green is on twelve. Red indicates thirty six minutes. Blue indicates eighteen [minutes] = 3 + 3/5 [hours] = 3:36
c) Red is on twelve = 3:36
d) Red is on twelve = 8:24.
Also, keep in mind that the watch can be rotated upside down as well.
A man is surviving on an island along with his friend. They have been starving from four days for food. Suddenly, they find a fisherman. The friend goes with the fisherman in order to catch the fish (if they can find any).
The fisherman returns after some time but he is alone and have some salmon that he had prepared. When asked, the fisherman tells him that his best friend fell off the boat and drowned in the water. Starving for so long, he eats the meal while crying for his friend.
After being rescued, he goes to a diner and orders salmon. When he eats his meal, he jumps commit suicide. Why did he do it?
After tasting the salmon, he realized that what he ate on the island was not salmon but probably the flesh of his best friend.
Check the figure given with this question. You have a square. What you have to do is cut and reassemble the square such that you create a Red Cross sign that has the same volume as that of the square.
The figure given is self-explanatory. But if you are unable to understand, here is what we did. We cut along the lines and remove the blue parts. Now rotate the paper a bit and place the cut parts like it is shown.
There is a boat with a brick of gold and a brick of iron. Both the blocks are exactly 10 inch in size. If they are dropped into the surrounding water of river.
Which one of the blocks will make the water level higher?
The iron block will make the water level higher.
In actual terms, none of the block will make the water level higher. This is because, while in the boat, they have a larger effect on the water level and they are raising it. But, when they are dropped in the water, they will actually make the water level drop. But, the iron block will make the water level drop much less than the gold block because it is lighter and will have less effect on the water from the boat but will displace the same amount of water as the gold one when dropped into the water.
This is basically a game of Tic-Tac-Toe which you all might have played innumerable times. Here, we are playing with the black and white markers instead. Also, there is a bit change to the rules. The changed rules allows you to play just three times. After the three markers are put by each of the players, you can only slide your marker into an empty square that shares a common wall with the square that the marker is leaving.You can refer to the figure given. If this is the position of the game, the white's next move would be from 6 to 3. Now, whatever the black does, the white one will move his marker from 5 to 2 and he will have a three in a row.What you have to decide is if both of the players are using a perfect strategy, will the white player (who plays first) always win? Or it will be the black one who will win always? Or every game will be a draw?
Let us try and make the white win when black's first move is to a non-corner square. White begins at 5 and black places its first marker at 2. White puts at 9 and black puts at 1. White plays at 3. Now if black puts at 7 to block, white will move from 5 to 6 and will win. But in this game, black can only play his last marker at 6. White can't win on the next move as his market at square 9 won't be able to get to square 7 in a single move. But white cam get to square 7 before black can block him or win. White will move from 8 to 7 to win the game. Thus, white can always force a win if he starts from the center of the square.
See the given image carefully. What you have to do is move the blue checkers in the position of the black checkers and vice versa. You are only allowed to move the checker to an adjacent empty space. Do it in the least possible moves.
1 -> 4
6 -> 1
2 -> 6
5 -> 2
4 -> 5
Of course, you can do in a different manner, this is just one of the possible solution with least number of moves.
There is a Pi picture attached here. We have given dotted lines over the places where you have to cut it. Now you will have five different pieces. Can you join these pieces in a manner that it becomes a square?
Here is one of the way to do it. Can you find any other way?