Android's lock screen feature allows people to protect their phones by joining points on a grid to make a pattern. Let be the size of the longest possible length of the pattern that can be drawn on an android phone with a pattern lock. If the grid is spaced equally by one unit what is rounded to the nearest integer?
The rules for drawing a pattern are:
You can only use a point once
You cannot "jump" a point if it is in between the two points and is part of the line that satisfies the first two points. Ie You cannot go from 1 to 9 without also hitting 5. But you can go directly from 2 to 9 without including any other point.
ONCE a point is "taken", it may THEN be skipped. A point cannot be skipped "in transit" only if it hasn't already been taken.
To fully understand the rules, it is best to try them out on a real phone.
Details and Assumptions
The points are equally spaced vertically and horizontally by one unit.
If it had been a grid, would be .