If $\text{\&}+2\text{\&}+\text{\&\&}+1\text{\&\&}=2\text{\&}4$, then what digit does $\text{\&}$ stand for?

Let the symbol $\text{\&}$ represent a single digit $x$. We can express the numbers according to their place values:
* $\text{\&}=x$
* $2\text{\&}=20+x$
* $\text{\&\&}=10x+x=11x$
* $1\text{\&\&}=100+10x+x=100+11x$
* $2\text{\&}4=200+10x+4=204+10x$

Now, set up the given equation:

$$x+(20+x)+11x+(100+11x)=204+10x$$

Combine like terms on the left side:

$$(1+1+11+11)x+(20+100)=204+10x$$

$$24x+120=204+10x$$

$$24x-10x=204-120$$

$$14x=84$$

$$x=\frac{84}{14}=6$$

Therefore, $\text{\&}$ stands for $6$.