|Spoiler Inside: Solution to Puzzle||SelectShow>|
There are two corned beef—cheddar cheese—Swiss cheese sandwiches. Since three sandwiches have both types of cheese, there must be one cheddar cheese—Swiss cheese sandwich.
There is at least one of each type. If there is only one each of the corned beef, corned beef—cheddar cheese, and corned beef—Swiss cheese sandwiches, then there are five sandwiches with corned beef which is the case so this must be.
This leaves three cheddar cheese and two Swiss cheese sandwiches.
In summary, there are three cheddar cheese sandwiches; two each of corned beef—cheddar cheese—Swiss cheese and Swiss cheese; and one each of the rest.