In the sum ⊗ + 1 ⊗ + 5 ⊗ + ⊗ ⊗ + ⊗ 1 = 1 ⊗ ⊗ for which digit does the symbol ⊗ stand?

The correct option is 3.

Let us find the single digit represented by the symbol ⊗. We can represent the symbol ⊗ as a variable $x$, where $x$ is a digit from 0 to 9.
Let us write down each term in the sum in terms of its place values:

1. The first term is ⊗, which equals $x$.
2. The second term is 1⊗, which equals $10+x$.
3. The third term is 5⊗, which equals $50+x$.
4. The fourth term is ⊗⊗, which equals $10x+x=11x$.
5. The fifth term is ⊗1, which equals $10x+1$.
6. The right-hand side is 1⊗⊗, which equals $100+10x+x=100+11x$.

Now, let us sum the left-hand side terms together:

$\left(x\right)+(10+x)+(50+x)+\left(11x\right)+(10x+1)$

Combine the constant terms and the coefficients of $x$:

Constants: $10+50+1=61$
Coefficients of $x$: $1+1+1+11+10=24$

So, the sum on the left-hand side is equal to $24x+61$.

Equating the left-hand side to the right-hand side:

$24x+61=100+11x$

Subtract $11x$ from both sides:

$13x+61=100$

Subtract 61 from both sides:

$13x=39$

Divide by 13:

$x=3$

Thus, the symbol ⊗ represents the digit 3.