Step 1: Water hardness reflects how much dissolved $Ca^{2+}$ and $Mg^{2+}$ salt content the water carries. The question asks which listed salt fails to add to that load.
Step 2: Soluble bicarbonates give temporary hardness. Both calcium bicarbonate and magnesium bicarbonate dissolve readily and are knocked out by heating, so they qualify as hardness-producers.
Step 3: Sulphate and chloride salts such as calcium sulphate give permanent hardness that boiling cannot clear. So calcium sulphate also counts as a cause.
Step 4: Calcium carbonate, by contrast, has very low solubility in ordinary water and stays as a precipitate rather than dissolving. Because it is not present in dissolved form, it cannot raise hardness. Therefore the odd one out is calcium carbonate.
\[\boxed{\text{Calcium carbonate}}\]