Distinguishing between inputs containing precisely M ones versus M+Δ ones demands an unexpectedly high number of oracle checks. This work demonstrates a lower bound of Ω(max{ζ√((N-M)(M+Δ))/Δ, √(ζN/Δ)}), a measure of computational effort linked directly to input size and desired accuracy. The analysis tracks individual query progress using a novel multiplicative adversary method.