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 ?
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??
Hello, cedricc!
There is nothing wrong with Listing the cases and looking for a pattern.Find the number of ways of tiling a rectangle with and 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 rectangle, so on),
but the number increases very quickly and starts getting quite confusing.
It also doesn't solve how many possibilities in terms of .
How do i solve this, showing working where possible?
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 . . .
.
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