by Bill Graham

Arthur is the painter and lawyer.
Betty is the engineer and teacher.
Charles is the doctor and writer.

Here's a start on working out this answer. The letters show which combinations are eliminated by each clue. You may find a better way to solve these problems. This approach is very systematic.

	doctor	engineer	teacher	painter	writer	lawyer
Arthur			a		a
Betty				f	e
Charles				f
doctor	—		b	d
engineer		—		c
teacher	b		—		a
painter	d	c		—
writer			a		—
lawyer						—

Note that the painter cannot be Betty or Charles and so must be Arthur. An asterisk in the next table indicates this match. Arthur is not a teacher or writer because of clue a, so the writer has these attributes also. The a' indicates these deductions from clue a given additional information. Looking at the painter row or column, you see the painter must be a lawyer. So, Arthur is the lawyer. The asterisks have been added below. Furthermore, Arthur (the painter and lawyer) cannot be a doctor or engineer. Add an 'x' in each appropriate cell to indicate no match. Don't forget that the lawyer is not the teacher, etc. from clue a. Add some more a' markers. Also, Betty and Charles are not the lawyer -- more x marks.

	doctor	engineer	teacher	painter	writer	lawyer
Arthur	x	x	a	*	a	*
Betty				f	e	x
Charles				f		x
doctor	—		b	d		x
engineer		—		c		x
teacher	b		—	a'	a	a'
painter	d	c	a'	—	a'	*
writer			a	a'	—	a'
lawyer	x	x	a'	*	a'	—

You should be able to fill in the rest yourself.