A large box contains 50 blocks which are either white, red, or blue. There are 11 times as many white blocks as there are blue blocks. There are fewer red blocks than there are white blocks, but there are more red blocks than there are blue blocks. By how much is the number of red blocks smaller than the number of white blocks?

Let's break down the problem:

1. Let's denote the number of blue blocks as B, the number of white blocks as W, and the number of red blocks as R.

2. According to the problem, there are 11 times as many white blocks as there are blue blocks. So, we can write this as: W = 11B.

3. The problem also states that there are fewer red blocks than there are white blocks, but there are more red blocks than there are blue blocks. So, we can write this as: B < R < W.

4. The total number of blocks is 50, so we can write this as: B + W + R = 50.

5. Now, we can substitute W = 11B into the equation from step 4 to get: B + 11B + R = 50, which simplifies to 12B + R = 50.

6. Since B < R, we can assume that B = 1 (the smallest possible value for B that still allows R to be greater than B). Substituting B = 1 into the equation from step 5 gives: 12(1) + R = 50, which simplifies to R = 50 - 12 = 38.

7. Substituting B = 1 into the equation from step 2 gives: W = 11(1) = 11.

8. Finally, to find by how much the number of red blocks is smaller than the number of white blocks, we subtract the number of red blocks from the number of white blocks: 38 - 11 = 27.

So, the number of red blocks is 27 less than the number of white blocks.