Question 7
In the first configuration, the numbers $11,22,33,44$ are placed in the boxes. Two paths start at the marked dots and follow arrows and dotted segments. The sum of the digits in boxes along each path is shown below it. The shaded box is the only box on neither path.
Now place $11,22,33,44,55,66,77,88,99$ into the boxes of the second configuration. Six paths follow the same rules, and the shaded box is again the only box on no path. What is the sum of all the different possible digits that can be placed in the shaded box?
Now place $11,22,33,44,55,66,77,88,99$ into the boxes of the second configuration. Six paths follow the same rules, and the shaded box is again the only box on no path. What is the sum of all the different possible digits that can be placed in the shaded box?