Hi,
I was playing this game in which you start from any cells of a 3x3 or 5x5 square and draw a line that loops through every cell in the box. The line can go only through a vertical or horizontal side (not diagonally). When you start from certain cells (problem cells), you can't reach at least one cell. In the attached file, I have shown such paths. The cells that can't be reached are shown with a question mark.
I am trying to find out how to express mathematically a.) why a particular cell can't reach every cell in a box, and 2) how many problem cells will be in a nxn matrix, where n is an odd number.
This is what I have noticed so far:
1. With even numbered squares such as 2x2 and 4x4, have no problem cells.
2. The 3x3 square has 4 problem cells and the 5x5 square has 12 problem cells.
3. Corner cells and the center cell (in the case of 3x3 and 5x5) are never problem cells.
4. The problem situation occurs when the line enters a T junction with empty cells on either sides.
How should I approach this problem?
Thanks.
I was playing this game in which you start from any cells of a 3x3 or 5x5 square and draw a line that loops through every cell in the box. The line can go only through a vertical or horizontal side (not diagonally). When you start from certain cells (problem cells), you can't reach at least one cell. In the attached file, I have shown such paths. The cells that can't be reached are shown with a question mark.
I am trying to find out how to express mathematically a.) why a particular cell can't reach every cell in a box, and 2) how many problem cells will be in a nxn matrix, where n is an odd number.
This is what I have noticed so far:
1. With even numbered squares such as 2x2 and 4x4, have no problem cells.
2. The 3x3 square has 4 problem cells and the 5x5 square has 12 problem cells.
3. Corner cells and the center cell (in the case of 3x3 and 5x5) are never problem cells.
4. The problem situation occurs when the line enters a T junction with empty cells on either sides.
How should I approach this problem?
Thanks.
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