Sometimes, some problem teaches us how to focus on a problem and think of it differently.. Actually, these kind of observations just make me wondered..

For example : 6x -3 this is equation can be seen as 3(2x-1) which means if we put integer values of x then this equation will give us multiple of 3. So these kind of querys like if it is possible to obtain a value V from this equation putting some integer values of x ; can be observed from this equation.. When I was in high school, I didn’t think over any equations. Just solved them. But observing any equation is much more important. While thinking over such problems i only note down what kind of new observations I got that could help me in future.

I want to know more From you. Hope it will actually help new problem solvers. I also want some observations observed by you that may help others to think over a problem more precisely and accurate way. Which observations made you wondered and pleased and made you think "OMG! this can be viewed like this! Couldn’t think of it "

Thanks for sharing your observation. I found one problem as you mentioned on second approach ; may be from Code chef. But I was not too clear about that approach. :/