You can do something the brute force way, the stupid, grind-the-problem-down-until-its-not-a-problem-anymore way ,or you can find the right approach and suddenly the problem just goes away. You look at the problem the other way and you have this epiphany: It was only a problem because you were looking at it in a wrong way.

There is a story of Carl Friedrich Gauss, the great mathematician which illustrates the above point. Gauss was in his school and his teacher was bored, so to keep the students preoccupied he instructed them to add up all the numbers between 1 to 100 .The teacher expected them to take all the day doing it.But the budding mathematician came back 5 minutes later with the correct answer:5050.

The solution is not to actually add up all the numbers, because that would be so frustrating and stupid. What he discovered was that by adding 1 to 100 it is 101 , 2 to 99 it is 101. 3 to 98 it is 101 and so on 50 to 51 it is 101..There are 50 such pairs and 50 times 101 is 5050..

The point is clear. Smart thinker doesn’t solve a problem the long and boring way because he sees what the real pattern is behind the question and applies that pattern to find the answer in a much better way.