Pattern Approach
This method can be used if there is a pattern can be detected when a set of data is collected. This is a popular method
for resolving statistic related questions.
The step of using pattern approach is:
- Collect the list of data and search of pattern
- Use the pattern to form a conjecture or hypothesis (assumption) and solve the problem
Example
Find the total number of square on a 4 x 4 checkerboard.
Yes, you can resolve it by counting the number of squares but this is not systematic and you may actually
miss out on some squares or duplicate counting on it. A more systematic way is to find out how many types of squares
In fact, if you study carefully, there are 4 types of squares:
1-unit square
2-units square
3-units square
4-units square
To resolve, we can calculate in this way:
1 -unit square: 42 or 4 x 4
2 -unit square: 32 or 3 x 3
3 -unit square: 22 or 2 x 2
1 -unit square: 12 or 1 x 1
So we sum them all together:
(16 + 9 + 4 + 1) = 30 squares.
As you can see, the number of squares for each type (1 -unit square,ect) is a square number. (42,32,22,12) and that form a pattern. This approach can be used
for problem that has repeated similar properties or pattern.
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