One (or more) ships can be placed because they are common to all possible placements.
Example
There are six possible positions to place a cruiser:
· (B,2) - (B,4)
· (G,2) - (I,2)
· (H,4) - (J,4)
· (H,8) - (H,10)
· (H,10) - (J,10)
· (J,6) - (J,8)
(Placing a cruiser at (B,8)-(B,10) would close off too many squares along row H).
Examining the board, you can see that there are five valid ways to place the two remaining cruisers:
· (B,2)-(B,4) and (J,6)-(J,8)
· (G,2)-(I,2) and (J,6)-(J,8)
· (H,4)-(J,4) and (J,6)-(J,8)
· (H,8)-(H,10) and (J,6)-(J,8)
· (H,10)-(J,10) and (J,6)-(J,8)
A cruiser at (J,6)-(J,8) is common to each of the five placements. Therefore, a cruiser must be placed at (J,6)-(J,8).
Example (virtual ships)
The above board has three virtual cruisers remaining to place (one battleship and two cruisers). There are six valid virtual cruiser positions:
· (B,3) - (D,3)
· (C,1) - (E,1)
· (C,3) - (E,3) [Remember, a virtual cruiser can be part of a battleship!]
· (D,1) - (F,1)
· (H,1) - (J,1)
· (H,3) - (H,5)
(There are two non-valid virtual cruiser positions: (H,3)-(J,3) and (H,5)-(J,5). Placing a virtual cruiser (i.e. three segment wildcards) at either of these positions would have completely closed off column 4, which must have one ship segment).
In how many ways can the three remaining virtual cruisers be placed on the board? Here are the four valid ways to place them:
· (B,3)-(D,3), (C,1)-(E,1) and (H,3)-(H,5)
· (B,3)-(D,3), (D,1)-(F,1) and (H,3)-(H,5)
· (C,1)-(E,1), (C,3)-(E,3) and (H,3)-(H,5)
· (C,3)-(E,3), (D,1)-(F,1) and (H,3)-(H,5)
A virtual cruiser at (H,3)-(H,5) is common to the four valid placements above. No matter how we place the three virtual cruisers, there must be one at (H,3)-(H,5).
Typically, you place a virtual ship by finalizing all the squares as wildcards. In our case, the virtual cruiser is a real cruiser.
Notice how we were able to deduce the placement of a ship by looking for all virtual cruisers, something we could not have done had we tried to place only real cruisers.