Permanent hardness in water cannot be cured by:

First, let us understand what permanent hardness in water means. Permanent hardness is caused by the presence of dissolved chlorides and sulphates of calcium and magnesium, such as $$\text{CaCl}_2$$, $$\text{MgCl}_2$$, $$\text{CaSO}_4$$, and $$\text{MgSO}_4$$. Unlike temporary hardness (which can be removed by boiling), permanent hardness does not precipitate out when the water is boiled.

Now, we need to check each option to see which method cannot remove permanent hardness.

Option A: Treatment with washing soda. Washing soda is sodium carbonate ($$\text{Na}_2\text{CO}_3$$). When added to hard water, it reacts with the calcium and magnesium salts to form insoluble carbonates. For example: $$ \text{CaCl}_2 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 \downarrow + 2\text{NaCl} $$ $$ \text{MgSO}_4 + \text{Na}_2\text{CO}_3 \rightarrow \text{MgCO}_3 \downarrow + \text{Na}_2\text{SO}_4 $$ This precipitation removes both temporary and permanent hardness. Therefore, this method can cure permanent hardness.

Option B: Ion exchange method. This method uses ion exchange resins, which are polymers that can exchange ions. The resin (usually sodium-based) swaps sodium ions for calcium and magnesium ions. For example: $$ 2\text{R-Na} + \text{Ca}^{2+} \rightarrow \text{R}_2\text{Ca} + 2\text{Na}^+ $$ $$ 2\text{R-Na} + \text{Mg}^{2+} \rightarrow \text{R}_2\text{Mg} + 2\text{Na}^+ $$ This process removes the ions causing permanent hardness. Hence, this method can cure permanent hardness.

Option C: Calgon's method. Calgon is sodium hexametaphosphate ($$\text{Na}_6\text{P}_6\text{O}_{18}$$). It forms soluble complexes with calcium and magnesium ions, preventing them from causing hardness. The reaction is: $$ \text{Na}_6\text{P}_6\text{O}_{18} + \text{Ca}^{2+} \rightarrow \text{Na}_4[\text{CaP}_6\text{O}_{18}] + 2\text{Na}^+ $$ This complex does not precipitate, so permanent hardness is removed. Thus, this method can cure permanent hardness.

Option D: Boiling. Boiling is effective only for temporary hardness, which is due to bicarbonates. When heated, bicarbonates decompose to insoluble carbonates: $$ \text{Ca(HCO}_3)_2 \rightarrow \text{CaCO}_3 \downarrow + \text{H}_2\text{O} + \text{CO}_2 \uparrow $$ However, permanent hardness salts like $$\text{CaCl}_2$$ or $$\text{CaSO}_4$$ do not decompose upon boiling. They remain dissolved and do not form any precipitate. Therefore, boiling cannot remove permanent hardness.

Hence, the correct answer is Option D.