The problem involves determining the number of different non-overlapping ways to cover a (2 x 10) rectangle using (1 x 1) and (1 x 3) rectangles. Participants are exploring combinatorial methods to approach this covering problem.
There appears to be productive exploration of the problem, with participants sharing their calculations for the (1 x 10) rectangle and discussing how these might relate to the (2 x 10) case. While there are differing figures presented, the conversation is ongoing without a clear consensus on the final count.
Participants are working under the constraints of not overlapping rectangles and are attempting to derive a solution based on previous findings. There is mention of a potential error in calculations that has been acknowledged and corrected by one participant.
sharpycasio said:Homework Statement
In how many different non-overlapping ways can a (2 x 10) rectangle be covered by (1 x 1) and (1 x 3) rectangles.
Homework Equations
The Attempt at a Solution
I've never done any question like this. The only solution I can think of is a brute force method but I doubt that's the way it is intended to be solved. Any hints? Thanks.
Mark44 said:Since the smaller rectangles can't overlap the larger (2 x 10) rectangle, you can simplify matters by looking at how you would cover a 1 x 10 rectangle with 1 x 1 squares and 1 x 3 rectangles.