Utkrisht123

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A boy sells oranges from door to door.
One day while on his rounds he sold 1/2 an orange more than half his orange to the first customer. To the second customer he sold 1/2 an orange more than half of the remainder and to the third and last customer he sold 1/2 an orange more than half she now had, leaving her none.
Can you tell the number of oranges he originally had?
Oh by the way he never had to cut an orange 
Think about these  Back to the Paradoxes
1. Let's say (hypothetically) there is a bullet, which can shoot through any barrier. Let's say there is also an absolutely bulletproof armour, and nothing gets through it. What will happen, if such bullet hits such armour?
2. Can a man drown in the fountain of eternal life?
3. Your mission is to not accept the mission. Do you accept?
4. This girl goes into the past and kills her Grandmother. Since her Grandmother is dead the girl was never born, if she was never born she never killed her grandmother and she was born.
5. If the temperature this morning is 0 degrees and the Weather Channel says, "it will be twice as cold tomorrow,".... What will the temperature be?
6. Answer truthfully (yes or no) to the following question: Will the next word you say be no?
7. What happens if you are in a car going the speed of light and you turn your headlights on?
8. I conclude with this challenge:
Let the God Almighty create a stone, which he can not pick up (is not capable of lifting)!
1. The world will end as infinite amount of energy will release (Big bang). Or Infinte amount of heat or energy transfer will take place.
2.No.
3.Yes I accept the mission of never the accept the mission.
4.This explains why time travelling is not possible.
5.Less than 0°
In my opinion "twice as cold" doesn't mean "twice the temperature" as sometimes it will increase the temperature making it less colder. eg 32°F will give 64°F
6.This one is really confusing.
7. Headlight will break. or Headlight will glow but no one will able to see its light.
8. I have to think on this one.

In a classroom of standard of VIII somebody wrote an equation on a blackboard ; to the left of the equal sign is one symbol, and to the right three symbols. A boy remarked that if the symbol to the left of the equal sign were inverted and one of the three symbols to the right were erased, the equation would still be true and it contains no redundant or unnecessary symbols. What is the equation?
(The line in a fraction counts as a symbol)
 1

Mr. D always followed the advice to conserve energy as he was a conscientious driver. While driving his family Ford one day, he came to a stop sign and noticed that the odometer showed 25952 miles. Observant as he was he recognised that the number was a palindrome. He thought that it will be a long time before a palindromic number happens again. Yet two hours later when he arrived home the odometer showed a new palindrome number.
What was the new palindrome number, and how fast was he travelling in those two hours?

In an interview, the interviewer asked a candidate about a four digit number whose first two as well as last two digits are perfect squares.
The conversations between the interviewer and the candidate are as follows
Interviewer : Can you tell me what number I am thinking of ?
Candidate : No I am not sure.
Interviewer : There are no zeroes in the number.
Candidate : I am still not sure
Interviewer : There is no repetition of digits.
Candidate : Sorry, I am not sure even now.
Interviewer : OK the sum of digits is a prime number.
Candidate : Sorry.
Interviewer : The first two digit number is bigger than the last two digit number. And no digit is 5. If you still don't know then I am sorry you may leave the room.
Candidate : Yes sir, now I know the number.
Can you tell what the number is ?

Shouldn't it be a 1/2 as one child is a girl and that another child can be a boy or a girl.

This is same thing as
Which is greater no mounatin or Mount Everest?
No mountain
" No mountain is greater than Mount Everest" 
The mother should say "You will eat my child"

I always wonder what is 0^{0}?
Is it 0, 1 or not defined or infinity

I need help in level 50 of triogical
 2

A and B played a game with some amount. They agreed that whoever will lose have to give half his amount to the winner.
They played 100 games and a result was that A won First game B won next two games A won next three games and so on
A B B A A A B B B B A A A A A...............
Who will have graeter amount after the 100th game?

All of you know that a^{2 } b^{2} = (a+b)(ab)
I know only two method to prove it.
a^{2 } b^{2 }a^{2 } b^{2}
a^{2 } b^{2 }+ ab  ab a^{2 } b^{2} + 2ab 2ab 2b^{2}
a^{2 }+ ab  ab  b^{2 }(a+b)^{2}  2b(a+b)
a(a+b)  b(a+b) (a+b)(a+b)  2b(a+b)
(ab)(a+b) (a+b)(a+b2b)
(a+b)(ab)
Apart form these two method are there any other method to prove it.

1 factors 1, 1 sum =2 i.e. 2*1
1 has only 1 as a factor so sum is 1

Perfect numbers are number whose sum of factors are twice the number itself.
Example
1. 6 factors of 6 are 1,2,3 and 6 sum=12 i.e 2 * 6
2. 28 factors 1,2,4,7,14,28 sum=56 i.e 2 * 28
can you tell any other perfect no?

Look at this pair
42 24 ( digits of 42 are interchanged i.e =24)
x 48 x 84 (digits of 48 are interchanged i.e = 84)
 
2016 2016
When the digit of multiplicand and multiplier are interchanged then also the result is same.
How many such pair can you find?

Groupone: 83,7,4,5
Grouptwo: 91,2,6
Good can you find one more
to get marked as best answer because there is one more competitor.
First one to give one more solution will be marked best answer

Group 1: 18,9,3,6
Group 2: 27, 4,5
both add up to 36
Good can you find one more
to get marked as best answer because there is one more competitor.

1 2 3 4 5 6 7 8 9
Arrange these numbers into two separate groups so that they add up to same total.
Note : you cant turn 9 upside down and make it 6
You have to turn the 9 into a six.
Numbers 19 total 45, which can't be evenly split.
Making the 9 a 6 reduces that total by 3 to 42.
So we need two groups that each total 21.
1 2 3 4 5 6 and 6 7 8 should do it.
Or turn the 6 into 9, increasing the total by 3 to 48.
1 2 3 4 5 9 and 7 8 9 do it for that case.
There is one solution in which you don't have to turn 6 into 9 or 9 into 6
The one who will give me that answer will be marked as best answer
So common guys give it a try

1 2 3 4 5 6 7 8 9
Arrange these numbers into two separate groups so that they add up to same total.
Note : you cant turn 9 upside down and make it 6

The stipulation that all 31 rectangles are “of the same size” is still a bit ambiguous. The size could be interpreted as area. If rectangles were equal that would imply they are equal in area (2 squares each) and dimensions. However, do we need a stipulation that rectangles must be alined on square boundaries?
If rectangle's dimensions were specified as 1x2, then the problem would be solved by googon97 in post #5.
But those rectangles could be 1/3 x 6, or 1/2 x 4. Still, it is impossible to cover up the board with 31 of those rectangles.
Furthermore, can we prove that we could or could not cover the board with 31 equal area (2 squares each) rectangles of any dimensions?
If you want to then You are welcome to do so

Two diagonally opposite corner squares are removed from a regular chessboard. Now is it possible to cover all 62 squares with exactly 31 rectangles ( no rectangle should overlap each other ).
If yes then how? If no then why?
yes,because you didnt say the sides of rectagles should be aligned with the sides of the squares
Good point.
i didnt thought that way
But if I say that all rectangles should be completely aligned and should be of same size then what would you say.

7, 63, 215, 513, 999
Carefully observe the pattern of series and tell
a) Which no. is incorrect in the above series?
b) What will be the correct no in that place?
c) What will be the next two numbers in the above series?

Two diagonally opposite corner squares are removed from a regular chessboard. Now is it possible to cover all 62 squares with exactly 31 rectangles ( no rectangle should overlap each other ).
If yes then how? If no then why?

Did you mean edges or faces?
Its the faces
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