A $$16$$-quart radiator is filled with water.Four quarts are removed and replaced with pure antifreeze liquid.Then four quarts of the mixture are removed and replaced with pure antifreeze.This is done a third and a fourth time.The fractional part of the final mixture that is water is． 
Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants
After the first time:$$1\times \frac{12}{16}+0\times \frac{4}{16}=\frac{3}{4}$$.  After the second time:$$\frac{3}{4}\times \frac{12}{16}+0 \times \frac{4}{16}= \frac{9}{16}$$.  After the third time:$$\frac{9}{16}\times \frac{12}{16}+0 \times \frac{4}{16}= \frac{27}{64}$$.  After the fourth time:$$\frac{27}{64}\times \frac{12}{16}+0 \times \frac{4}{16}= \frac{81}{256}$$. 