A pattern code in a cell phone can be created by using three line segments to join one point each in 3 rows with 3 points.
If the three segments should form a continuous line how many possibilities are there.
The pattern code is created using 3 line segments that join one point in three rows with 3 points each. It is also required that a continuous line is formed by the three segments.
The number of different patterns can be determined in the following way. First consider the three points in the lowest row, the points at the ends can be connected to 2 points each in the middle row and the point at the center can be connected to all the 3 points in the middle row. Similarly, if a point at the ends of the middle row is used it can further be connected to 2 points each and if the center point is used it can be connected to any of the 3 points in the top row. The total number of patterns that follows from this is: 1*1*2 + 1*1*2 + 1*1*3 + 1*1*3 + 1*2*2 + 1*1*3 = 2 + 2 + 3 + 3 + 4 + 3 = 17
There are a total of 17 patterns that can be created.