### Sample Problem

A, B and C each likes one of Basketball, Volleyball and Football and each studies at one of Columbia, Duke and UCLA. We have these clues:

(1)   A does not study at Columbia;

(2)   B does not study at Duke;

(3)   This UCLA student does not like Football;

(4)   The one who studies at Columbia likes Basketball;

(5)   B is not the guy who likes Basketball.

Which sports do they like and which college do they study at?

A: , B: , C: ,

#### Solution

We turn to a table for help:

(Note: √ means viable while × means not)

Since (1) , A is not in Columbia, we mark a × in that cell;

Since (2) , B is not in Duke, we mark a × in that cell;

Since (5) , B does not like Basketball, we mark a × in that cell;

Since (1) and (4) , A does not like Basketball, we mark a × . Thus C likes Basketball and we mark a √ in that cell and × in his other two cells.

Since (4) , C is in Columbia rather than Duke, we mark a √ and a × in the two cells respectively. Thus A is in Duke, we also mark a √.

Since (3) , B does not like football, that’s a × , thus B likes volleyball and A likes football.

Here is the completed table:

From the table, we can tell that A is in Duke and likes football; B is in UCLA and likes volleyball; C is in Columbia and likes Basketball.

In problems like this, a table can greatly simplify the work you have to do.