Maths Puzzles

 The number 121 is a perfect square in any number number system with base greater than 1. That is because the product of 11 and 11 in any number system is 121.   The answer is 121  All the numbers in the sequence are 16 in different number system. First one 10 is 16 in hexadecimal number system. 11 is 16 in number system with base as 15. Next one 12 is 16 in base 14 number system and so on. So our answer is 16 in base 3 = 121.

1. The number 121 is a perfect square. In a decimal system. In which other number system, is 121 a perfect square?           Bonus : Let us look at another puzzle based on different bases. 2. What is the missing number in the following sequence: 10, 11, 12,13, 14, 15, 16, 17, 20, 22, 24, 31, 100, - - , 10,000. (Hint: The missing number is in ternary notation)  Find the solutions to these puzzles here .  

 Here was the puzzle 91.   John inherited from his uncle 25% more money than his sister Helen. He wants to give her part of his money to have the same amount as her. What percentage of his money should he give to Helen? Let us say that John's sister inherited x rupees.   John inherited 25% more than her. Let us say his inheritance is y. y = 0.25x + x = 1.25x x = y/1.25 The extra amount received by John is 0.25x Extra amount = 0.25x = 0.25 X  y/1.25  = y/5 = 0.2 y To divide this equally among both, he has to give half of this amount to his sister.  John should give 0.2 y/2 = 0.1 y = 10% of y to his sister.

John inherited from his uncle 25% more money than his sister Helen. He wants to give her part of his money to have the same amount as her. What percentage of his money should he give to Helen?   Find the solution here.