Pigeon Holing

n = 10;
allocations = RandomChoice[Range[n], n + 1];
endx = {};
Do[
  endx = Append[endx,
    Length[Select[allocations[[i ;;]], # == allocations[[i]] &]]]
  , {i, n + 1}];
Manipulate[ Graphics[Join[
   Table[{ColorData["DarkBands"][i/(n + 1)],
     Disk[{0, i} + t ({7 - 0.5 endx[[i]], allocations[[i]]} - {0, i}),
       0.25]}, {i, 1, n + 1}],
   {Red, PointSize[Medium]},
   Table[Point[{0, i}], {i, n + 1}],
   {Blue},
   Table[Point[{7, i}], {i, n}]
   ], PlotRange -> {{-1, 8}, {0, n + 2}}],
{t,0,1} ]