Answer
The least multiplicity is the smallest coefficient which is 1
Work Step by Step
When the 4 particles are in the box with two sides, left and right, the polynomial configuration is $(1+x)^n$ and $n=4$. To find its multiplicities, we need to expand the configuration.
$(1+x)^4 = (1+x)^2 (1+x)^2$
$(1+x)^4 = (1 + 2x + x^2)(1 + 2x + x^2)$
$(1+x)^4 = (1 + 2x + x^2 ) + (2x + 4x^2 + 2x^3) + ( x^2 + 2x^3 + x^4)$
$(1+x)^4 = 1 + 4 x + 6x^2 + 4x^3 + x^4$
So the least multiplicity is the smallest coefficient which is 1
