A method for detecting the presence or absence of multiple HPV target nucleic acids in a sample, wherein said HPV nucleic acids are from two or more strains in a set of strains of HPV, said method comprising: a) treating said sample with a pool of probe sets in a single reaction, wherein each of said probe sets comprises a first oligonucleotide and second oligonucleotide configured to form an invasive cleavage structure with said target nucleic acid, wherein i) said pool of probe sets comprises probe sets configured to form an invasive cleavage structure with target nucleic acid from at least two different strains of HPV in said set of strains of HPV, and ii) for each different strain of HPV in said set of strains of HPV, at least two of said probe sets are configured to hybridize to at least two different regions of each HPV target nucleic acid to form an invasive cleavage structure with target nucleic acid from the strain; under conditions wherein said probe sets will form invasive cleavage structures if target nucleic acid is present; b) determining the presence or absence of formation of at least one invasive cleavage structure in said sample in an invasive cleavage assay configured to detect at least one HPV nucleic acid and exposing the sample to the detection assay under conditions such that at least one HPV nucleic acid can be detected, wherein a fluorescence resonance energy transfer (FRET) cassette configured to generate a detectable signal in a FRET assay in response to a cleavage of the first oligonucleotide in said invasive cleavage structure is used, thereby detecting the presence or absence of HPV nucleic acids from at least one strain from said set of strains of HPV in said sample, and wherein said pool of probe sets is selected from the group of pool sets as indicated in the table below and wherein the 1 st oligonucleotide is indicated as Probe and the 2 nd oligonucleotide is indicated as Invader: or a) treating said sample with a pool of probe sets in a single reaction, wherein each of said probe sets comprises a first oligonucleotide and second oligonucleotide configured to form an invasive cleavage structure with said target nucleic acid, wherein i) said pool of probe sets comprises probe sets configured to form an invasive cleavage structure with target nucleic acid from at least two different strains of HPV in said set of strains of HPV, and ii) for each different strain of HPV in said set of strains of HPV, at least two of said probe sets are configured to hybridize to at least two different regions of each HPV target nucleic acid to form an invasive cleavage structure with target nucleic acid from the strain; under conditions wherein said probe sets will form invasive cleavage structures if target nucleic acid is present; i) said pool of probe sets comprises probe sets configured to form an invasive cleavage structure with target nucleic acid from at least two different strains of HPV in said set of strains of HPV, and ii) for each different strain of HPV in said set of strains of HPV, at least two of said probe sets are configured to hybridize to at least two different regions of each HPV target nucleic acid to form an invasive cleavage structure with target nucleic acid from the strain; b) determining the presence or absence of formation of at least one invasive cleavage structure in said sample in an invasive cleavage assay configured to detect at least one HPV nucleic acid and exposing the sample to the detection assay under conditions such that at least one HPV nucleic acid can be detected, wherein a fluorescence resonance energy transfer (FRET) cassette configured to generate a detectable signal in a FRET assay in response to a cleavage of the first oligonucleotide in said invasive cleavage structure is used, thereby detecting the presence or absence of HPV nucleic acids from at least one strain from said set of strains of HPV in said sample,