A costume party is going on in a class of a few students. The average of the boys (b) is g and the average age of the girls (g) is b. If the average age of all of them including their class teacher who is 42 years old is b+g.
Can you find the value of b+g?
8
for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)
(b,g)=(3,5) => b + g=8
You are playing a probability game with your friend using a fair coin. Both of you decide a particular sequence that you have to achieve.
Let us suppose you chose the sequence to be: H T H
Your friend chose the sequence to be: H T T
Now you keep tossing coin until you get the sequence and the same is done by your friend. You keep doing that till you achieve your predefined sequence and keep writing the result on paper. At the end of the game the player whose average number of tosses will be lowest, he will win.
The results of game 1 toss:
You: H T T H T H
Your score: 6
Your friend: H T H H H T H H T T
Your friends' score: 10
The results of game 2 toss:
You: T T H T T H H T H
Your score: 9
Your friend: T T H H T H T T
Your friends' score: 8
The results of game 3 toss:
You: T T H H T H
Your score: 6
Your friend: H H T H T T
Your friends' score: 6
Now after 3 games, your average score is 7 and your friend's average score is 8. Now assume that you keep playing the game and play many a times. What will be the possible outcome out of the following?
a) You win
b) Your friend win
c) Tie
Analyzing thing, the friend has better chances of winning. Let us assume and analyze what can happen at any point of time supposing that we have not already completed the sequence. If the last flip was tails, start at 1 and if it is heads, start at 2.
1) If any one between us flips to get tails, nothing will change. We will still be at step 1 and we both will be needing 3 additional flips to complete. But if either of us gets heads, we continue.
2) If either of us gets heads, we stay on this step. But if we get tails, we continue. At this point, I am 3A and my friend is 3B.
3A) If I get tails now, I will have to start all over again from step 1 till I again get heads and I will have to flip the coin at least 3 times to complete my sequence.
3B) If the friend gets heads, he goes back to the step 2 and try again for tails. He will have to flip the coin at least 2 times to complete his sequence.
Thus, he obviously has better chances of winning.
How many triangles can you find in this given picture?
There are 20 triangles in the picture.
Do you know of a place where the wind blows south and then suddenly shifts direction towards the north ?
The place is the South Pole. Until the point the wind reaches the pole, it is going south but the moment it passes the pole, it is going north.
Ten frogs are sitting on a log floating on the surface of a river. Two of them decides to jump off in the water.
How many frogs are there on the log at this moment ?
Ten frogs only. The two frogs have just decided to jump, they have not jumped till now actually.
These type of puzzles are known as charade. What you have to do is find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.
Just for an example, if my first refers to 'off' and my second refers to 'ice', then my whole will be office.
My first is present - future's past -
A time in which your lot is cast.
My second is my first of space
Defining people's present place.
My whole describes a lack of site -
A place without length, breadth, or height.
NOWHERE
The two words hinted are:
NOW (The present time)
HERE (The present place)
Combining them, we get NOWHERE (A lack of place).
If Japan and Panama decided to merge into a single country, probably people will name it Japanama.
Can you think of two more such countries unions that could produce similar names like Japanama by overlapping their three letters?
Of course there can be many others, but here are two for you:
Russia and Belarus ---> Belarussia
Sweden and Denmark ---> Swedenmark
A murder has been committed in a house. You are a detective and have to find out the murderer.
You investigate by asking three questions to each of the six suspects. Out of those six suspects, four are liars. It is not necessary that they speak everything a lie. But in their answers, there must be at least one lie. One of the six is the murderer.
There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.
At the time of the murder, only the murderer was present in the killing room. Any number of people can be present in any of the other rooms at the same time.
Can you identify the murderer and the four liars? Also can you find out who was in which room?
The responses of all the suspects are mentioned below.
Joseph:
Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.
Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
But I think that Joseph was in the living room, OH MY GOD!
Peter:
Mandy was in the kitchen with Christopher.
But I was in the bathroom.
David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.
Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.
Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.
PS: The corpse was found in the Living Room.
Assume that Peter is not in the second bedroom. This suggests that Joseph, Mandy, David and Christopher are liars. This further suggests that Peter and Jennifer speak truth. But they cannot be as they do not correspond on Christopher's location. Hence we have assumed wrong and Peter is in second bedroom.
By saying that, we have established that Peter is in the second bedroom. Also, Peter and Jennifer are liars
Assume that Joseph speaks truth. This suggests that David is in the bathroom and Joseph in the second bedroom. This further suggests Mandy and David are liars as they told that Joseph was not in the second bedroom. Also suggests that Christopher lied, as he said David is in kitchen. Therefore, there are three new liars, totaling 5 liars, which is a contradiction given the situation in the question.
Thus, we have established that Joseph is a liar
Assume that Mandy speaks truth. This suggests that Joseph was in the living room and David in the Kitchen. This further suggests that David and Christopher are liars. But again, this contradicts as we have concluded that there are again 5 liars (including above 3 established liars)
Thus, we have established that Mandy is a liar. David and Christopher speak truth. Jennifer was in the bathroom. Joseph was in the first bedroom. David was in the kitchen. Christopher was in second bedroom with Peter.
The killer has to be Mandy as no one else was present in the living room
