My son asked me how to solve this question which was part of his Primary 1 maths worksheet:

Question: How many triangles are there in the figure below?

Try to solve the problem first and than scroll all the way down for the solution.

The answer is 14. Here is the solution: 

My wife & I could not solve it but later on I realized that there is a technique to it and it is based on a systematic approach to the counting of the number of triangles.

How long did you take to solve the problem? If you know the technique, it should take within a couple of minutes. If you do not know the technique, it could take hours to solve using “brute force” method. Perhaps it remained unsolvable to some unless you know the technique.

I recalled that when in my first job as an R&D Engineer, I was implementing a firmware to locate the motion vectors between two adjacent frames of a motion picture. It was a compression algorithm. There are a lot of duplicate data between two adjacent frames. The key is to determine which part of the frame has moved. For brute force method, it will require a search of  8x8=64 times assuming a search area of 8 by 8 pixels. (If my rusty brain did not failed me) there are sub-optimal ways to reduce the search to just 3 times or it is often called 3-steps algorithm. Because of a drastic reduction in computation, it translate to cost saving because there is no need to use powerful DSPs.

Financial planning is like that too. There are two ways to do financial planning. Some will self study and do it themselves. These are what we call the “brute force” method. It is slow and tedious. Also, if you do not acquire the necessary skill, there are “triangles” that remained uncounted. That is to say that there could be lapses in one’s financial well being that remained unnoticed. The second method is to outsource completely to a financial planner to do it. But the problem is that the financial planner is a technical person too and unless the client understands, the planner cannot “force” the client to understand the plan.

The third way is the recommended way – which is that the client must seek to understand and take charge of his financial well being and seek assistance from a financial planner to help him. Let the financial planner teach him the techniques and provide the necessary information. In this way, the client will acquire skills… to count triangles (just joking).