(* the initial amounts *)
amounts={a,b,c,d,e,f,g}; 
For[ii=1,ii≤Length[amounts],ii++,
(* ii wins the game *)
amountToPay=Total[amounts]-amounts[[ii]];
amounts[[ii]]=amounts[[ii]]-amountToPay;
For[jj=1,jj≤Length[amounts],jj++,
If[jj!=ii,amounts[[jj]]*=2]
]
Print[Simplify[amounts]]
]

NSolve[Table[Simplify[amounts[[ii]]]==32,{ii,1,7}],
{a,b,c,d,e,f,g}]