Solution:

If $x<1$, the equation becomes $(1-x)=(2-x)+(3-x)$ which simplifies to $x=4$, contradicting the assumption $x<1$.

If $1 \leq x \leq 2$, we get $(x-1)=(2-x)+(3-x)$, which gives $x=2$.

If $2 \leq x \leq 3$, we get $(x-1)=(x-2)+(3-x)$, which again gives $x=2$.

If $x \geq 3$, we get $(x-1)=(x-2)+(x-3)$, or $x=4$.

So $2$ and $4$ are the only solutions, and the answer is $2$.