problem

Problem solving There are many ways to solve a problem and we can use heuristics to solve a complicated mathematics problem.

Some heuristics for solving problems are:

change your point of view
make an organised list
work backwards
make a supposition
trial and error
think of a related problem
simplify the problem
eliminate the unlikey possicilities
draw a diagram

There are of course many others heuristics but now let us look at a problem and see what we can do to solve it.
How many zeroes are there?

                                                  0
                                                0 0
                                              0 0 0
                                            0 0 0 0
                                          0 0 0 0 0
                                        0 0 0 0 0 0
                                      0 0 0 0 0 0 0
                                    0 0 0 0 0 0 0 0
                                  0 0 0 0 0 0 0 0 0
1 layer= 1              =1
2 layers= 1+2         =3
3 layers= 1+2+3     =6
4 layers= 1+2+3+4 =10

We can see that there is a number sequences. The number of that particular layer was added by the previous layer to het the amount of zeroes. Example:

4 layers= the number of zeroes for 3 layers is 6 and add 4 to 6 you will get 10 and the amount of zeroes is indeed 10 for 4 layers. We have to find a formula to get the answer and the formula is to take the number of that particular layer and add one to it. After adding one, take the number of that layer and mulitply it by the number which was added by one. After getting the answer, divide it by 2 and you will get the number of zeroes.

Problem solving requires the skill of spotting pattern and even though some patterns may not make sense to you sometimes, as long as you have the formula, you can find the answer. Always remeber to simplify a problem first before finding a pattern.

The End

David Lim Yurui(16)