Some problems from NMTC level 2 junior contest, conducted in India by the AMTI. Try to solve 'em all! And please post solutions, like, and re-share!
1 [NMTC 2011]
If , , , and , find the value of
2 [NMTC 2011]
, , and are real numbers such that and . The difference in maximum and minimum possible value of is . Find .
3 [NMTC 2012]
Find all positive integral solutions to the equation
4 [NMTC 2012]
Consider the set of numbers . We delete any two numbers and from the set , and replace them with a single number . What number will be left at the end, after such operations. Will the number always be the same?
5 [NMTC 2013]
Find positive real solutions which satisfy both these equations: and .
6 [NMTC 2013]
Do there exis distinct integers, such that the sum of any nine of them is a perfect square?