Given the numbers between 1 and 1 million, what is so special about the number 40 that it makes the number stand out of the crowd ?
The number 40 (Forty) is the only number which when written in English has all the letters in the same order as in the alphabets.
The measurement of time
That cant be found on a clock
But can be looked upon on a map
Who am I ?
I am Mississippi.
(One Mississippi, Two Mississippi, Three Mississippi etc.)
Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea.
Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee ?
The fact is that both the amounts are same.
After the swap has been done, you must know that the quantity of liquid is same in both the cups as you have taken and mixed a spoonful only in both the cases. So, there is no change in the quantity of the liquids.
No if there is any tea missing from the tea cup, it is now in the coffee cup. Also, since the quantity is same, then the same amount of coffee must be missing from the coffee cup and is now in the tea cup.
Can you find out the remainder when 3^300 is divided by 5?
3
It is obvious that it is not feasible to calculate 3^300 as it will take too much of time. So we will use a trick to solve the question. We will calculate the remainder of each power till we find a pattern.
3^1 divided by 5 leaves the remainder 3.
3^2 divided by 5 leaves the remainder 4.
3^3 divided by 5 leaves the remainder 2.
3^4 divided by 5 leaves the remainder 1.
3^5 divided by 5 leaves the remainder 3.
3^6 divided by 5 leaves the remainder 4.
As you can see that the pattern is now repeating itself and it will go on like this till 3^300 and beyond. Since every fourth remainder is same as the first, we will look for the power of 4 only. 300 is divisible by 4. Therefore at the power of 300, the first remainder will repeat itself and the remainder will be 3.
Can you find a number that lies one third of the distance between 1/3 and 2/3?
Let us find a bigger multiple first. Lets multiply the numerator and denominator by 9 in both the numbers.
Now, 1/3 = 9/27
And, 2/3 = 18/27
Clearly, 12/27 lies one third on the distance between the two numbers now.
Below, you will find the mathematical proof that 10 equals 9.99999…. But is that possible or there is something wrong about it? Can you find the error?
x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10
No error is present in this proof and 10 is actually equal to 9.99999…. The proof is absolutely correct.
A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."
Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"
The truth is that it was not. How did the grand children know it?
The word "World War I" could not have been engraved on the sword. This is because the Second World War had not happened then and nobody knew that it will happen.
Can you think of three numbers that gives a prime number as their product and also the difference between the second and first is equal to the difference between third and second?
The three numbers are: -3, -1 and 1.
Remember that we never asked for positive numbers.
A special integer exists in mathematics that shows a special property. If you subtract any number from that integer, the result will always be divisible by the successor of that number completely.
Do you know what that integer is ?
The required integer is -1.
For an example, let us subtract 7 from -1.
-1 - 7 = -8
Now the successor of 7 is 8 and (-8) is exactly divisible by 8.
You can try that for any number and it will hold true.
Can it be possible to build a house that has all its four walls facing towards the South?
Yes, it is possible.
If the house is built at the North Pole, all the walls will face towards South.