# Trail passing through squares of a grid

Let's construct a 10x10 grid. 0n the 100 squares you are allowed to place 7 bases (the red dots in the diagram below) in any square on the grid. Then you fill the grid with skinny trominoes. The trominoes have to cover all the squares except the squares which contain a base. Next, construct a continuous trail (the red line on the diagram below) which passes through all 7 bases. The trail is not allowed to cut any of the trominoes and is allowed to pass through each square only one time. Also, the trail is allowed to make only one angle within each square. What is the maximum number of squares through which the trail can pass? Below is an example.

• Do we need to find a new combination of dots which maximisies the value, or in thea bove dots only Commented Mar 23, 2021 at 2:30
• In the above soln with 42 squares covered ,I think you can increase the value more than 42 also Commented Mar 23, 2021 at 2:31
• @AakashMathur As stated in the question, the bases (dots) can be anywhere on the grid. The goal is to increase the number of squares through which the trail passes.. Commented Mar 23, 2021 at 2:39
• My gut feeling is that it is possible to pass through all 100 squares, but could be tricky to find. Commented Mar 23, 2021 at 11:48