I have been blessed with four wings but I am unfortunate as I cant fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.
Do you know what I am ?
I am a windmill.
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.
As you see in the picture, there are four 3-link chains. All you have to do is join them into a big 12-link chain. For joining two closed links, one of the links must be cut and placed onto the other link for closing.
How many minimum links will you have to cut to make the big chain ?
Just 3.
Refer the picture. All you have to do is cut three links from a single 3-link chain and then you can use them to join three other 3-link chains to make a big 12-link chain
A man found the English Channel while sitting on his sofa. How did he find it?
He was searching on a map and located it between France and England.
Andrew was absent from school for most of the days and thus the principal called him. He asked Andrew for an explanation to which Thomas replied the following:
I don't have enough to attend school. I must have eight hours of sleep every day and if added for 365 days, it makes 122 days in a year. We have weekends off adding to 104 days of the year. The summer holidays are roughly 60 days. I take an hour for each meal adding to 3 hours a day and 45 days a year. I must spend 2 hours every day for exercising and recreation to stay physically and mentally fit which adds up to 30 days in a year.
If you add all of them, you will get 361 days as the answer. So I am left with only 4 days to attend the school.
Though the principal knows that Andrew is messing with his head, he is unable to point where Andrew is going wrong. Can you tell how he is calculating in a wrong manner?
Fore mostly, Andrew is adding up a lot of double count7s. He is adding the time spent sleeping, eating and relaxing etc. separately while without deducting that time from the weekends and other holidays. Also, weekends occur is summer holidays as well. Thus these hours are being counted several times.
Another thing is that the school does not happen for 24 hours and thus the 4 days will count as 16 days of school even if a school commence for six hours.
what dies below science rebus means ?
Ag Ag Ag
Ag SPOON Ag
Ag Ag Ag
silver spoon
