**Background**

World is overloaded with problems. People are talking only about problems all the time so they are not getting enough time to think about solutions. As we talk more about a problem, that problem becomes famous and looks like a complex problem. There is a general assumption that only complex solutions can solve complex problems. As the complexity of the problem is projected very high, common man does not try to solve the problem. So these problems are left to the great people.

I feel that there exists a simple solution for every problem. There exists a simple solution for every complex problem. Sometimes the solution is so obvious that people ignore to take it as a solution.

I have decided to give simple solutions to all world problems. With these solutions, I hope, people will get new line of thought to solve problems.

**Simple solutions solve the problem. Complex solutions create business.**

The following are few examples of how people get carried away with the complexity of the problem where a simple obvious solution exists.

**Swelling in baby’s cheek**

One day baby of my relative got a swelling in cheek. I also went to the paediatrician along with them. The doctor was very famous paediatrician in the city. We did not have appointment so we had to wait for 3 hours. After long waiting we went inside, a junior doctor checked and noted down the details. After some time the famous doctor came, checked the details and checked the baby. Then he said, “Just put little salt or sugar in to the baby’s mouth, the swelling will come down”. We asked, “Any tablets to take?” He said, “Not required”. We came out, paid the consultation fee and came back home. My relative started shouting and scolding the doctor, “Waited for so long time, paid so much money and he had not given a single tablet, what doctor he is”, and so on.

When people think the problem is complex, they expect the solution also to be with similar complexity. If you give simple solution, they cannot believe that it works.

If the same doctor gives a prescription of 4 medical tests (blood, urine, etc), one anti-biotic, a pain killer, a balm to apply on skin, few more medicines (to be used in case the baby gets fever, vomiting or headache), then the people will be very happy. They think that the doctor understood the problem that’s why he prescribed everything properly. In small towns and villages, some of the doctors who have their own lab and medical stores give this type of prescriptions. If you get the tests done in some other lab, the doctor simply says the reports are wrong, get it done again.

**Astronaut problem of writing**

There was an astronaut-meet. One American astronaut and one Russian astronaut were sitting together. (I am using the same country names as I read in the story. Please take the moral, not the names.) The American started telling about one of the problems that they faced while writing with pen in the space. “The pens that we use work with pressure and gravity. As we write, the ink comes down because of the gravitational force. But in space, there is no gravity. So our pens will not work there. We raised the problem. One company took that contract and created a battery operated pressure pen. It creates pressure at back side of the refill and constantly pushes the ink to front. We used that pen for our space mission.” said the American proudly. With a pause, “You might have also faced this problem. How did you solve it?” he asked. The Russian replied, “We used pencil”.

**Don’t create new problem to solve a problem**

One day a stingy person goes to his relative’s house. A child was carrying a tincture bottle from one room to other and the bottle slips. Bottle was broken and all tincture was on the ground. Our stingy person thought, “The tincture is getting wasted, somehow it has to be utilized”. Immediately he got a brilliant idea, took a blade, cut skin of his own hand and applied all the tincture on that.

**Four parts of a square**

It is a puzzle or a problem. It shows how fast we get used to complexity and don’t come back to simplicity.

The following problems need to be solved in the given order and should not jump to a problem without solving all previous problems. The problems are:

1. Divide the unshaded part of block number 1 in to 2 equal parts.

2. Divide the unshaded part of block number 2 in to 3 equal parts.

3. Divide the unshaded part of block number 3 in to 4 equal parts.

4. Divide the unshaded part of block number 4 in to 5 equal parts.

Out of the box thinking

a. Cover all 9 dots with 4 connected straight lines

b. Infinite line through a Sphere

One day in Computational Geometry class, our professor asked us whether we could define an infinite line that could pass through the centre of the sphere without touching the surface of the sphere. None of us thought that was possible. Then the professor asked one more question. We could give answer immediately. With the answer of second question, we understood that the first question was extension of the second question and we could give answer for first question also.

Sometimes we think that it is impossible to solve a problem till we find a solution or a clue. Remember, “Everything is possible”. We need to try a little longer. That’s all.

**Curve and line intersection**

In earlier days of my career, I was given a project. The project has computation part and visualization part. We got 2.5 months time. I was given the visualization part as I was graphics expert. Computation part was given to other two engineers. They need to solve the problem of finding all the intersection points of a 3D NURBS curve and a 3D line. Both the engineers were experts in CAD and non-linear geometry. I was new to non-linear geometry at that time so not involved in their discussions.

As they knew that NURBS curve was very complex and could not be handled directly, they quickly found an algorithm that converts a NURBS curve in to multiple cubic Bezier curves. So the problem boiled down to finding the intersection points of a cubic Bezier curve and a line.

They searched internet thoroughly and found two suitable algorithms. But one of them cannot guarantee correct solution always. It randomly fails. The other one is approximation algorithm. It guarantees the solution but it takes huge number of iterations to reach the required tolerance level. So it is very slow for the application. The two engineers took the algorithms one each and started improving them as they could not get any other algorithm. Now and then they kept on searching internet for better algorithm or technique that can solve their problem.

2 months got over. I completed my work. Other two engineers were more or less at same stage as they started. Though I didn’t know much about those algorithms, I decided to help them whatever way possible. I discussed about the problem that they were trying to solve. My idea was to mix these two algorithms and write a new one by taking the advantages of both. That was on Friday. That weekend, I was thinking about the problem at home. I got a doubt in my mind, “When both curve and line are having equations, why is Mathematics not solving the problem?” Immediately I took a white paper and a pen, wrote the equations and solved them by using my school days’ algebra. I got the solution before reaching end of the page. Mathematics cannot go wrong because that is my favourite subject.

Monday morning, I reached office and implemented my algorithm. I did not tell anybody about my solution. If it does not work, they will make me a fool. Because two engineers with my level of experience were working and a senior engineer with about 10 years of experience in this field was helping them to solve the problem. If I give so simple solution and it does not work, it will be very embarrassing. I implemented my solution and checked the values. I was getting all proper values. But with numbers I cannot guarantee whether it is exact solution. So I quickly added intersection points in to my visualization. I got proper intersection points at all zoom levels. I went to my boss and explained the story. My boss said, “It is good but it may not work for non-uniform curves”. He may be right. I have not considered non-uniformity in my equations. I went back to my desk, added non-uniform equations also in to my algorithm. I checked everything visually. Everything was working perfectly. I asked my boss whether we can patent it. He said, “It is obvious solution. It cannot be patented”. It is so obvious solution that people ignored to consider it as a solution.

The project was successful with highest performance, no extra memory usage, correctness up to the machine precision and on-time delivery.

The moral of the story is: whatever the world is talking about the most is not the final solution. If you get a solution in the internet, it may not be the best solution. If you don’t get a solution in the internet, that does not mean there is no solution. For every problem, there exists a simple solution. If you find a solution but not simple, that means you are still on the way to reach simple solution.

## Any questions?