Brown, Jones and Smith are a doctor, a lawyer, and a teacher. The teacher, who is an only child, earns the least money. Smith, who married Brown's sister, earns more than the lawyer. What is each man's job?(answer below)
One way to solve almost any of this whole class of problems (which can get extremely complicated) is to make a grid with the names in one direction and the occupations in the other. Then one by one eliminate cells in each row or column from the facts given. When all but one of a row or column is filled in, then fill in the rest of the corresponding row and then continue. I have seen whole books of just these kinds of problems, which seems boring to me because once one learns this technique, they can all be solved the same way. I only include one of these problems and this is it. Let's do this problem to see how it works.
For example, start with the following table:
| Doctor | Lawyer | Teacher | |
| Brown | |||
| Jones | |||
| Smith |
Then mark an X in impossible cells. Smith cannot be the lawyer, nor the teacher.
| Doctor | Lawyer | Teacher | |
| Brown | |||
| Jones | |||
| Smith | X | X |
Then, when only one possible cell remains in a row or column, mark an O there and then fill in the rest of the remaining column or row. That is, once we know that Smith is the doctor, we know that Brown and Jones are not the doctor.
| Doctor | Lawyer | Teacher | |
| Brown | X | ||
| Jones | X | ||
| Smith | O | X | X |
Now continue crossing off impossible cells. Brown cannot be the teacher:
| Doctor | Lawyer | Teacher | |
| Brown | X | X | |
| Jones | X | ||
| Smith | O | X | X |
Now that only one cell remains possible in both row one and column three, each must be an O.
| Doctor | Lawyer | Teacher | |
| Brown | X | O | X |
| Jones | X | O | |
| Smith | O | X | X |
The puzzle is now solved because there is an O in each row and column. If you really feel the need to, you may place an X in the middle cell, but the puzzle is already solved at this point. That is, from the table you can see that Brown is the lawyer, Jones is the teacher, and Smith the doctor. This method might seem like overkill for this simple problem, but once you learn how to draw these grids, you can solve the hard puzzles, like identifying the positions of nine named players on a baseball team. Let's move on to another whole class of problem.
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