This puzzle is an original, I'm sure it shares a similar idea with some other logic problems. However, I worked out the details of this one. I haven't put the [no-computer] tag because computer aid search can make the puzzle more accessible. A solution MUST NOT be based on purely computational methods, but rather on logical deduction you can explain and work out by hand.
Some good friends of mine recently became obsessed with logic and I can't take anymore of their games. It's always about Alice, Bob and Charlie somehow. I decided to craft my own little game that will keep them quiet for the rest of night. The base is that of a minesweeper but with a small twist. Take a look at the following grid:
What I plan on doing is handing this out to my four friends and tell them:
- "There are 4 bombs in this grid"
- "I've put flags on some cells. I can assure you that on those cells, there are no bombs and they all have at least one bomb in the 8 surrounding cells"
- "Behind the flags, there is at least four 1s, two 2s and one 3. Of course there can be more"
Then I will hand out to each one of them a special kind of glasses that reveal flagged cells that have the same value as the type of the glasses. So for example, I will give to player 1 the glasses of type 1, that can see cells that are flagged AND with a value of 1.
In this minesweeper, the goal is not to avoid bombs but rather to find the bombs. I will ask them to hand me a map of where they think the bombs are, and I will compare with the correct one. That gives me the advantage that if they are not sure of the emplacements of the bombs, i.e. multiple possibilities remain, I can swap with another valid map of the bombs and make my favorite logicians eat their hats. I should note that the flags are always in the same position as in the picture.
I figured it will be more fun to make them play by teams of 2, as it maximizes my chance to see them fail, but let them pick the teams knowing who has which glasses. At this point, I thought of 2 variants:
- In the first variant, within a team they can only communicate by saying whether or not they know all the bomb spots;
- In the second variant, the two members of one team can share their glasses, and use all the information of the pair to spot the bombs;
The question I have, is which one should I give them, to ensure at least one team can fail for at least one grid. Can you help me?
Hint 1:
I will not be able to play more than 22 rounds of this game. If this is too much let me know I can add some constraint to make it down to 10.