An altered MineSweeper

Question

I've been searching for an old project I did in college about a computer program to create and solve a special variation of the popular game MineSweeper where, instead of always one, you could have multiple bombs on the same cell and all the numbered cells are displayed at the very beginning of the game. And finally I found it! On one of the modules of the program I designed, you could setup a grid where an armed cell could support up to $3$ bombs. For instance, a 3 x 3 grid could be presented like this:

$\qquad\qquad$

To solve the MineSweeper all you have to do is fill the empty cells with 0, 1, 2 or 3 bombs so that each numbered cell is adjacent to its own number of bombs (adjacent my be horizontally, vertically or diagonally):

$\qquad\qquad$$\qquad\qquad$

As you can see, you may fill the empty cells with numbers instead of bomb drawings. Just be sure to distinct them from the initial filled cells.

So, my challenges for you are:

CHALLENGE 1. Can you fill the three next grids using, at most, three bombs for cell? (The three grids are independent from each other). This challenge is just an warm up!!

$\qquad\qquad$$\qquad\qquad$$\qquad\qquad$

CHALLENGE 2. Fill the next 8 x 8 grid using the same rules (at most, three bombs for cell):

$\qquad\qquad$

PLEASE NOTE: There is only one solution for each grid.

Answer 1

The small puzzles:

The first two are solved with very straightforward logic: find a cell with only one empty neighbor, fill it in, repeat.

The third requires slightly trickier logic: from the 3s, we know the middle column has 3 mines total. So the 6 on the left must have its other 3 mines above it. The same goes for the 5 on the right, and then we can fill in the other two numbers using the 6 clue at the top to help us.

The big puzzle:

This one doesn't require too much difficult logic. The strategies used are essentially the same ones as the small puzzles.

The right side can be filled in very easily. Each time, there's at least one clue that has all but one cell around it filled, so you can just fill things in:

Continuing...

you can make inroads into the center. Again, each time, there will be a clue with exactly one touching empty cell, so you can fill in that empty cell.

The only logic that's more complicated than that is the 3 I've added to the left column: you can get that from the 5 and 2 below it. The two empty cells on their right must contain 2 mines total (from the 2 clue), so the remaining 3 go to the 5.

And continuing further, you can finish off the puzzle. The final answer:

Answer 2

Challenge 1:

For the left grid I started by working with the 1 in the upper right corner, knowing that would place only 1 bomb in the very centre. From there looked at the 2s along the top to guarantee a 1 on the left of the centre space. Next looking at the 5 in the bottom left, since there is a total of two bombs above it, it needs 3 bombs to the right. This leaves 1 bomb for the the final space in the bottom right corner.
For the middle grid started with the 1 in the top left, the only space it can get a bomb is right below it so that must be a 1. That makes the space to the right of the 1 in the middle of the top row a zero. For the 3's and 2's to work you then need. 2 in bottom right.
For the right grid started by looking at the 3's along the bottom. It isn't possible for it to be 3 bombs in either middle space without making the 5 on the right or 6 on the top wrong, so it must be a 1 and 2. For the 5 and upper 6 to work it must be 1 in the middle, 2 on the bottom. This makes it a 2 on the upper right because of the 5 and a 3 on the upper left because of the 6's.

Challenge 2:

Starting at the bottom left there needs to be 2 bombs above the corner as it is the only spot the two in the bottom can touch bombs. From there you can work your way up solving for the bombs needed for the 4, 5, and 3's along the right side. At the bottom middle there is another 2 that only has 1 space for bombs so there must be 2 bombs there. Working through the middle can solve for the placement of bombs around the 7's and 10. Based on those numbers it must be zeros in the upper left. This gives you the information to solve for the 2 in the middle left and from there you can work your way down the left side.