Question

Has anyone been able to find a solution to "Problem set#3, Problem 6A - Computer Word choose" (http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-00sc-introduction-to-computer-science-and-programming-spring-2011/unit-1/lecture-7-debugging/MIT6_00SCS11_ps3.pdf ) that runs in less than polynomial time? Is it even possible, given the problem?

Answer 1

if you have seven letters in your hand and you want the computer to find the best word,
you have to check every permutation of the seven letters "taken" 2, 3, 4, 5, 6, and 7 at a time (k-permutations). don't think you can get around that.

The same problem for the 2008 course had an additional twist and led to another solution that let you get away with every Combination of the seven letters 'taken' 2, 3, 4, 5, 6, and 7 at a time (k-combinations).
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-00-introduction-to-computer-science-and-programming-fall-2008/assignments/pset6.pdf

Big difference between the number of permutations and the number of combinations and how they grow..

Then there is a solution that doesn't exactly use permutations or combinations and if I remember it is much faster - but i don't think that is exactly what they wanted. one purpose of the pset is to get you familiar with the size of the search space for those types of solutions..