MindMine #1

Logic Level 2

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: $\large{\begin{array}{|c|c|c|c|} \hline 1 & 2 & 3 & 2 \\\hline 2 & 3 & 5 & 3 \\\hline 1 & 2 & 4 & 2 \\\hline 1 & 1 & 2 & 2 \\\hline \end{array}}$ How many of the cells are shaded?

4 6 8 10 12

1 solution

Jonathan Quarrie
Apr 17, 2018

Green is confirmed as un-shaded. Orange is confirmed as shaded. Yellow is unconfirmed. (x,y)

To resolve (1,1):
- If (1,2) is shaded, then (4,1) could not be resolved (due to (3,1) and (3,2) not being shaded - as a result of (2,1) being resolved).
- If (2,2) is shaded, then (4,1) could not be resolved (due to (3,1) and (3,2) not being shaded - as a result of (2,1) being resolved).
- Thus, we must shade (2,1).

Due to (1,2) already being resolved by (2,1):
- (1,3) and (2,3) must not be shaded.

To then resolve (1,3):
- (1,4) and (2,4) must both be shaded.

To then resolve (2,1):
- If (3,2) is shaded, then (4,1) could not be resolved (due to (3,1) being resolved - causing (4,2) to not be shaded).
- Thus, (3,1) must be shaded, and (3,2) must not be shaded.

To then resolve (3,3):
- (3,4) (4,4) (4,3) and (4,2) must be shaded - There are no other choices.

And finally (3,3) and (4,1) remain un-shaded.

There are $\large\boxed{8}$ (orange) shaded cells.

MindMine #1

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