The last solution was an example of vertical thinking.

Let us analyse the process.

- It depends heavily on logic.
- At every step, a mistake would spoil the process - this leads to what is called YES / NO logic
- It is repeatable i.e. the same procedure can be applied to any number of players
- It is teachable

It for the last reason that vertical thinking is popular in educational circles. One can teach procedures and then all the student has to do is to apply the process to problems he is given.

In examinations, the problems are specially chosen so that the process is applicable but in real life, this may not be the case. What does a student do when they process is not applicable. This is where other methods are needed