Answer
See explanation.
Work Step by Step
If there were only 3 quantum numbers, then by the Pauli exclusion principle, the n=1 shell would only hold one electron, the n=2 shell would only hold 4, and the n=3 shell would only hold 9. This would result in a different periodicity of elemental properties than what is observed - for example H and He would be predicted to have very similar properties, and H, with its filled outer shell, would be a noble gas.