Julia wants to build another garden wall, 10 bricks long and 3 bricks high. Can she build it with red and white bricks, so that no two bricks of the same color are next to each other?

r w r w r w r w r w
w r w r w r w r w r
r w r w r w r w r w
I say yes. Could you help me if this is correct. Thank you.

Yes that is correct.

Well, Julia's garden wall seems to have a nice pattern going on, like a colorful checkerboard. But let me get this straight... You want to know if the pattern she chose ensures that no two bricks of the same color are next to each other, right?

Hmm, let me think about it...

Ah, I cracked the code! It seems like Julia's pattern does indeed meet the criteria. If you look closely, each brick is surrounded by bricks of the opposite color. So, for every red brick, there's a white brick next to it, and vice versa. It's like a never-ending dance of colors!

So, congratulations! Julia can definitely build her garden wall using red and white bricks, without any two bricks of the same color being adjacent. Now your garden will not only be beautiful but also an excellent example of color coordination. Keep up the good work and happy gardening!

Yes, based on the pattern provided (r w r w r w r w r w), Julia can build the garden wall using red and white bricks such that no two bricks of the same color are next to each other. The pattern ensures that the colors alternate between red (r) and white (w) for each row. Therefore, she can proceed with building the garden wall according to the given pattern.

Yes, you are correct. Julia can build a garden wall using red (r) and white (w) bricks such that no two bricks of the same color are next to each other.

To determine this, we can use a method called the pigeonhole principle. In this case, the "pigeonholes" are the pairs of adjacent bricks, and the "pigeons" are the two available colors, red and white.

Since Julia wants to build a wall that is 10 bricks long, there will be 9 pairs of adjacent bricks. By using the pigeonhole principle, we can conclude that as long as Julia has at least 2 colors available (in this case red and white), she can always ensure that no two bricks of the same color are next to each other.

So, Julia can indeed build a garden wall using red and white bricks, following the pattern you provided:

r w r w r w r w r w
w r w r w r w r w r
r w r w r w r w r w

I hope this explanation helps!