Maths Puzzles

There are 5 consecutive even numbers whose sum is 640. Which are these numbers? e.g. 2,4,6,8,10 are consecutive even numbers and their sum is 30. Show answer The average of 5 consecutive even numbers will be equal to the third number. Because if the numbers are  x,x+2,x+4,x+6,x+8, then their sum is 5x+2+4+6+8 = 5x+20  Their average is (5x+20)/5 = x+4 which is the third number of the sequence.   Here the sum is 640 => average is 640/5 = 128   Hence the sequence is 124,126,128,130,132 

Is it legal in India for a man to marry his widow's sister? Justify your answer. A man living in a high rise building decides one day to go out of the window instead of door. He jumps from the window. But he survives the fall without a scratch, and continues to walk to his office. How is this possible? A man enters a room and presses a button. Immediately he is 10 kg lighter. However when he leaves the room, he is having his original weight. How?      Find the solutions here . 

 Three statements are made about the books owned by David. Thomas - David owns more than thousand books.    Richard : No, he owns fewer than that.   Harry : He certainly owns at least one book.  Only one of these three statements are true. Who is right?    Find the solution here .  

 What is the pair of numbers whose product is equal to the product of its least common multiple (LCM) and greatest common divisor (GCD)? You can find the solution here . Hint: The problem is much much easier than you think.  The GCD is the largest positive integer that divides each of two or more integers.   The LCM is the smallest positive integer that is divisible by both integers

In a room, there are 14 people who are blond and 8 people who are blue eyed. Five of these people are both blond and blue eyed. There are also two persons in the room, who are neither blond, nor blue eyed. How many people are in the room?   Solution : 19  There are 14 blonds and 8 blue eyed people. As 5 of these are both blonds and blue eyed,  Number of blonds but not blue eyed = 14-5 =9 Number of blue eyed but not blond = 8 - 5 = 3 Number of blond, eyed people = 5 Number of people who are neither blond, nor blue eyed = 2 So total number of persons in the room = 9+3+5+2 =  19