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| How Many L's CptS 355 - Programming Language Design Washington State University |
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How Many 'L's?
Goal: fill a 4x4 grid with letters such that each row (read left-to-right) and column (read top-to-bottom) is an English word and all the words are distinct. Find such a square with the maximum possible number of 'L's. Words formed by adding an 'S' at the end to changed between singular and plural may not be used.
We're going to write computer programs to help us solve this problem.
Group problem-solving exercise:
- What is a word? How can a program tell whether a particular sequence of 4 letters is a word or not?
- How many squares can be built by filling in each cell with each
possible letter?
- There are about 2500 4-letter English words. If we form squares by taking 4 of these words and stacking them up how many different squares can be formed? If it takes a millisecond to build and check each square how long will this process take? (Hint: this tells you something about how not to solve the problem.)
- There are about 500 4-letter English words containing at least
one 'L'? How many different squares can be formed by stacking 4 of
these? How long would that take? Would approaching the problem in
this way produce a solution?
- How might we obtain a list of English words? of 4-letter English
words? of 4-letter English words containing at least one 'L'?
- What are the constraints between the words? How could they be
exploited to reduce the amount of work?
- What are the symmetries in the problem? How could they be exploited to reduce the amount of work?