Number of Ways
Find the number of ways of tiling a "2 x n" rectangle with "1 x 2" and "2 x 2" tiles, given that the edges of the tiles are parallel to those of the rectangle.
I have tried listing ways but that was only working through examples (2 x 1 rectangle, 2 x 2 rectangle, 2 x 3, 2 x 4 and so on, but the number increases very quickly and starts getting quite confusing. It also doesn't solve how many possibilities for n assumably in terms of n. How do i solve this showing working where possible??
Hard to tell what's allowed:
as example, in a 2 by 2 rectangle, can you have these 5 ways:
1 2by2, or
2 1by2 placed horizontally, or
2 1by2 placed vertically ?
There is nothing wrong with Listing the cases and looking for a pattern.
Quite often, it is the only approach available to us.
I found this list . . .
I see this pattern: Starting with the third term,
. . each number is the sum of the preceding two numbers, plus 1.
That is: .
That's as far as I dare to go . . .
Originally Posted by Soroban
Considering, what "Wilmer" wrote, doesn't that mean there's more than three possibilities for a 2 by 2??
Whoops: I show 3 possibilities; my "5" is a typo; I'll repost:
as example, in a 2 by 2 rectangle, you can have these 3 ways:
1: one 2by2, or
2: two 1by2's placed horizontally, or
3: two 1by2's placed vertically
Soroban's is CORRECT (Rock)