World's Simplest Impossible Problem
Don Morrison, founder of New Mexico's C.S. Department, is credited with posing the "World's Simplest Impossible Problem."
The Problem: "I'm thinking of two numbers. Their average is 3. What are the numbers?"
What are your answers?
Cleve Moler, cofounder of The MathWorks, once discussed this problem, noting that some possible answers are 3 and 3, 4 and 2, 6 and 0, 23 and 17, or 2.71828 and 3.28172.
Then, Moler set up the software program MATLAB to solve the problem, using the marix equation A*x = b where A = [1/2 1/2] and b = 3. What do you think the technology produced?
First, using MATLAB's forward backslash, he typed x = A\b. The resulting solutions were 6 and 0.
Second, using the matrix inverse approach, he typed x = pinv(A)*b. The resulting solutions were 3.000 and 3.000.
To Moler and Morrison, this problem is simple to state but is impossible because it is illposed and does not have a unique answer. Yet, I find it interesting that technology is still able to produce answers.
Moler closes with this thought: "Now I'm thinking of three numbers whose average is pi. What are the three numbers?"
Source: "Cleve's Corner," MathWorks Newsletter, Dec. 1990.
