MindMine #4

Logic Level 3

In the grid below, the number in each cell represents the number of neighboring cells which are shaded, including the diagonals but not including the cell itself: $\large{\begin{array}{|c|c|c|c|} \hline 1 & 2 & 2 & 2 \\\hline 3 & 4 & 6 & 3 \\\hline 2 & 3 & 4 & 2 \\\hline 2 & 3 & 3 & 2 \\\hline \end{array}}$ How many of the cells are shaded?

6 7 5 4 8

1 solution

Saya Suka
Jan 20, 2021

This involved the minesweeper tactical strategies to fully explain things, and it's kinda difficult doing it with my limited English vocab and the lack of graphics as visual aids to at least bridge my meaning across.

Let's label the grids by rows and columns, bottom row and left column first while top row and right column last. If you can see a 6 on the intersection of the third column and the third row, we use the notation of (3,3)=6 and another example of (1,4)=1.

I mentioned the 6 and 1 because these are the extremities in this problem, and usually a maximum and a minimum of things are easily the simplest to handle due to the force by sheer number or bare nothingness.

Now, look at 1 & 3 from the first column, (1,4)=1 and (1,3)=3 to be exact. They both neighbours to each other, and 1 is placed at the corner. 3 would need 2 more shaded cells than 1 even at their proximity, so the extra two must be somehow 'hidden' from 1's views (direct reach / influence around 1). So our hands are forced to tuck them as far away from 1, and those would be at row 2, at (1,2)=2 and (2,2)=3. You have no choice but to place them there or else you risk sharing the unwanted shade with (1,4)=1.

This is how you start the journey, but I'll let you reach the destination on your own.

The answer is 7 shaded cells, 4 of them occupying the whole of row 2 and another 3 would be (2,3)=4, (3,4)=2 and (4,3)=3.

MindMine #4

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