Twelve constellations and nine squares gestures _ Twelve constellations and nine squares gestures

How many squares can I draw with a nine-grid gesture password?

The nine-grid gesture password can draw 389 1 12 patterns, and the specific analysis is as follows:

Jiugongge gesture password is different from ordinary digital password, and it has some special rules. To sum up, there are three aspects:

1, at least four points and at most nine points.

You can draw diagonal lines, but you can't jump points unless the middle point has been used. For example, you can go directly from 1 to 6, but you can't go directly from 1 to 3, but if you have already used 2, you can go directly from 1 to 3.

3. Don't reuse points.

Considering the problems of the above rules, it is inevitable that the Jiugongge gesture password cannot be a full permutation and combination of 1-9. For example: 1-3-7-5, 1-6-4-5, 1-7-6-4-5 and so on, these are all impossible passwords.

In the specific algorithm, an undirected graph with 9 nodes can be considered, and the edges satisfying the above rules can be connected. After traversing each node, traverse each level at the starting point. When the height is 4, count the number of leaf nodes. Each time the statistical results are accumulated and finally divided by 2, the total is 389 1 12.

Extended data:

Common nine-grid gesture passwords are as follows:

1, name: arrow in the lower left corner, and the gesture order of points is 3, 5, 2, 7, 6 and 5.

2. Name: the arrow in the upper right corner, and the gesture order of points: 7, 3, 6, 2, 3.

3. Name: Solitary darts, the gesture sequence is 9, 1, 6, 2, 4, 3, 7.

4. Name: chubby, soft and lovely arrow. The gesture sequence is: 4, 8, 9, 6, 2, 1, 7, 5, 3, 2.

5. Name: the soldier's bugle number. The gesture sequence is 1, 4, 8, 6, 3, 5, 7, 2, 9, 1.