Marilyn Oversimplifies these Equations with Shapes

Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."

In her Parade Magazine column of November 12, 2006, Marilyn suggests that if + 2 + = 9, and + + 2 = 12, then 2 + 2 = 14.

Sorry, Marilyn, but your answer is incomplete

You are correct that 14 is one solution, but you neglected to mention that there are an infinite number of additional solutions. This is a problem in which there are two equations ( + 2 + = 9 and + + 2 = 12) but three unknowns (, , and ). Based upon these two equations and three unknowns, we can determine that - = 3.

Some of the solutions are:

• = 6, = 0, = 3, and 2 + 2 = 18.

• = 0, = 2, = 5, and 2 + 2 = 10.

• = -3, = 3, = 6, and 2 + 2 = 6.

• = -6, = 4, = 7, and 2 + 2 = 2.

In fact, there are fractional solutions as well as the integer solutions listed above.